It seems certain Carrick will remain in charge for Sunday's trip to Premier League leaders Chelsea after overseeing Tuesday's Champions League tie against Villarreal.
There are then four days until Arsenal visit Old Trafford on 2 December and by then some clarity will surely have emerged around what, to outsiders at least, appears a pretty confused picture.
BBC Sport analyses the factors United's hierarchy are wrestling with as they seek to ultimately appoint a manager who can bring success back to the club.
Why do Manchester United want an interim boss?
In their statement confirming Solskjaer's exit, United said they were looking to appoint an "interim manager" to the end of the season.
The wording suggests United accept their preferred choices may not be available until the summer as they are already in work and do not believe Carrick, who has never been a manager, is a viable option to hold the position for the rest of the campaign.
Yet the strategy feels complicated and inherently means the club would be appointing a manager on the basis they will leave within as few as six months when they have found someone better.
Only realists, or older managers possibly not seeking a permanent job, are likely to find that scenario attractive.
Steve Bruce has been mentioned but, despite being a former United skipper, his last months as Newcastle manager are unlikely to inspire optimism among fans - and United have plenty of time and incentive to turn this season around.
Some may wonder if Sir Alex Ferguson, with more pedigree than anyone in the game, could be a luxury stop-gap - but the reality is the Scotsman is now 79.
The names already mentioned for the role - former United defender Laurent Blanc and seasoned coach Ralf Rangnick - already have jobs.
Blanc is manager of Al Rayyan in Qatar, where the season continues until March. Rangnick is technical director at Russian club Lokomotiv Moscow, who admittedly do take a 10-week winter break from the middle of December.
Lucien Favre has been out of work since being sacked by Borussia Dortmund in 2020. The 64-year-old has been linked with numerous Premier League jobs and was close to getting the Crystal Palace job in the summer before turning it down.
MOTD2: Solskjaer should be walking away with his head held high, says Jenas
Who is making the decisions?
Amid the fall-out from the European Super League debacle, United executive vice-chairman Woodward said he would stand down by the end of the year.
At the time, many felt that meant the summer. But Woodward remains in post and while it is highly unlikely he will sever ties with United completely when he does eventually stand aside, that has the potential to create uncertainty around negotiation.
United say Woodward is getting on with his job and they do have other people, negotiator Matt Judge for a start, who do some work around recruitment.
But for now, Woodward and his likely replacement, managing director Richard Arnold, are both involved and are understood to have been on the call with co-chairman Joel Glazer on Saturday evening when it was resolved Solskjaer had to go after the defeat at Watford.
Woodward was the man who delivered the bad news to Solskjaer in person and was also the man who asked Carrick to take temporary charge.
Mauricio Pochettino, whose Paris St-Germain side are top of Ligue 1, is understood to be open to a move to Old Trafford
Would United want Pochettino?
While those within Old Trafford defend their intended use of an interim manager until the summer, they acknowledge that if someone who was in their thinking to take over permanently became available, they would go for him now.
It is known former Tottenham boss Mauricio Pochettino is open to the idea of joining Manchester United. It is also felt Pochettino could be recruited now if United pushed for him given his unease at the structure around him at Paris St-Germain.
United officials have spoken in glowing terms around the Argentine previously and know what an outstanding job he did at Tottenham, certainly up until the 2019 Champions League final.
So, will United make a move?
It is not always clear what lies behind the club's major decisions. Antonio Conte, who quit Inter Milan last summer after winning Serie A, was unemployed and available on the day United suffered the 5-0 home defeat by Liverpool on 24 October that many felt should have triggered Solskjaer's dismissal.
Instead, they kept Solskjaer and in the meantime Conte has joined Tottenham.
The feeling was Conte would be too difficult to manage and the scars from the conflict that categorised the latter part of Jose Mourinho's time at Old Trafford remain.
Yet virtually no high-profile manager is easy to deal with. Ferguson wasn't, Pep Guardiola isn't, Pochettino probably wouldn't be either.
Pochettino feels he would get more power over the recruitment of players at United than he does in Paris. Would United's hierarchy be willing to provide that to someone who has yet to win a trophy in England and was in charge as PSG failed to secure Ligue 1 for only the second time in nine years?
Nevertheless, there are many, inside and outside Old Trafford, who feel Pochettino would be the perfect fit - now or in the summer. But no appointment comes without risk and there are certainly some attached to the popular 49-year-old.
Who else is in the frame?
If there are risks with Pochettino, they are even greater with some of the other candidates.
Brendan Rodgers has done an excellent job at Leicester for two seasons, securing fifth-place finishes in successive years and winning the FA Cup last season.
But this term is a different story. Their win over United on 16 October is one of only four victories in 15 matches across all competitions.
They were booed off at half-time in Saturday's home defeat by Chelsea, are in the bottom half of the table and need to beat Legia Warsaw in the Europa League on Thursday if they are to retain a realistic chance of reaching the knockout phase.
Add in Rodgers' Liverpool connection and it is perhaps not hugely surprising there are plenty of fans who harbour doubts about him.
At Ajax, Erik ten Hag has forged an impressive reputation, guiding the club to the 2019 Champions League semi-finals, where they looked certain to reach the final before Tottenham's stunning comeback in Amsterdam.
He has done this despite losing so many top-class players - including midfielder Donny van de Beek, who was chronically under-used by Solskjaer.
But the gap between Eredivisie and the Premier League is enormous. And Frank de Boer's ill-fated stint at Crystal Palace might not help his cause as United ponder what a Dutch manager could bring.
Zinedine Zidane is available now but has no interest in the job. Luis Enrique is unlikely to welcome any distraction to his World Cup preparations with Spain - and he won't be done with them until the end of next year, unless he decided to quit, which is not expected.
'Embarrassing... it's like Stenhousemuir' - pundits' reaction
Former Celtic, Blackburn and Chelsea striker Chris Sutton says United's wish to appoint an interim manager is "embarrassing", comparing their strategy to that of Scottish League Two side Stenhousemuir.
"It is amateur stuff," said Sutton on BBC Radio 5 Live's Monday Night Club. "They are going to have another trialist in. That is what Stenhousemuir do. If they pass the test, they give him a contract.
"It is embarrassing.
"This is the self-proclaimed biggest club in the world and they don't have a contingency plan. It is sheer panic."
Former Manchester City defender Micah Richards described the situation as "shambolic".
"We are talking about Manchester United here," Richards said. "They are not acting like the biggest club in the world.
"Ole deserves a lot of the flak but the board deserve the flak as well. How can this happen?
"They have someone [Carrick] with no experience at the helm. It goes from bad to ridiculous."
As Carrick said, the focus is on a Champions League game against Villarreal, where United must avoid defeat if they are to keep qualification for the knockout phase in their own hands.
After that it is Chelsea, a game United fans will approach with trepidation given the heavy punishment already inflicted on them by other top-three sides Liverpool and Manchester City.
Behind the scenes, the recruitment process continues. Club insiders are adamant they are working to a plan, even if, on the outside, it is not entirely obvious what that is.