Harlequins winger Lynagh, 20, was included in England's training camp for the first time last month.
"We'll see how things go there... and whether there's any interest in him to come back to Australia," said Rennie.
"Not until he's capped," added Rennie when asked if he has lost hope of luring Lynagh to the green and gold.
Lynagh, who scored two decisive tries in Harlequins' Premiership final win in June, qualifies for England, where he has lived since he was four, Australia and Italy, where he was born.
His father revealed in June that Australia and Italy had made approaches to Lynagh about his senior international future, but that at that time he had heard nothing from England, who he had represented at several different age-grade levels.
However, he was subsequently called into the England 45-man training squad.
"If I get the chance for England, Australia or Italy, I'll take it," Louis told Rugby World in January.
Once capped at senior level, players are effectively tied to a national team.
England play Tonga on 6 November, before matches against Australia and South Africa on the following weekends.
"Look, obviously Eddie's [Jones] well aware of his lineage and the need to catch him quickly," Rennie said.
Lynagh's 18-year-old brother Tom joined Queensland Reds from Harlequins last month, saying it is his dream to play for Australia in the 10 shirt his father once wore.