The Argentina international was carried off on a stretcher early in the first half of City's 3-2 win against promoted Southampton on the opening day of the Premier League season and has not played since.
After the City squad flew into the Spanish capital on Monday evening, Mancini said Aguero was now "okay".
"Probably he is not 100 per cent because he didn't play since the injury but the feeling at this moment is good," he told a news conference at Real's Bernabeu stadium.
"He has a chance yes," he added, when asked by a reporter if Aguero might play.
A hero to City fans after scoring the goal that clinched the league title last season, Aguero knows the Real players well from his stint at their city rivals Atletico.
He scored three goals against the current La Liga champions in 11 derbies but failed to win any of those games, suffering eight defeats and three draws.
Mancini did not reveal which of his four available strikers he would deploy on Tuesday, with Mario Balotelli, Carlos Tevez and Edin Dzeko also available.
Volatile Italian Balotelli has the same chance of playing as any of the others, he added.
Mancini, Real coach Jose Mourinho's predecessor at Inter Milan, was asked the inevitable question about the Spanish club's poor start to La Liga and comments by forward Cristiano Ronaldo that he was "sad" for professional reasons.
"If he (Mourinho) wants to win again La Liga he should send Cristiano for six months to Portugal and when he comes back they can win La Liga again," Mancini joked.
The packed calendar, with players only having a few weeks off between the end of the European championship and the start of the domestic season, may have contributed to Real's troubles, he added.
Mourinho's side lost 1-0 at Sevilla on Saturday and have taken only four points from their opening four matches to slip eight behind early leaders Barcelona.
Real have already lost twice, also slipping up at Getafe, equalling the number of defeats in the whole of their title winning 2011-12 campaign.
"I watched the (Sevilla) game, it was a difficult game," Mancini said.
"The first six, seven, eight games of the season (after a major championship) are really difficult, for Real Madrid, for us and for every club team," he added.
"We should be focused on the game and on our play and not this (Real's problems)".
Group D is completed by Borussia Dortmund and Ajax, who meet in Dortmund on Tuesday.