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 "OK".
"Probably he is not 100 percent 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.
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 football 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.
"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]".
