Manchester City captain Vincent Kompany could be out for up to two weeks after limping off with a calf problem during his side's Europa League defeat to Sporting Lisbon.
The Belgian international was replaced after just 12 minutes in Lisbon, and has been ruled out of the weekend trip to Swansea City.
However, the influential centre-back could not only miss the return leg with Lisbon in a weeks time, but also the league game against Chelsea in two weeks
Mancini said: "I hope he can recover in 10 days, two weeks maximum."
The Italian continued: "When you have a calf [injury], it can be a big problem. We will see how it is in another one or two days.
"I didn't take a risk with Micah because Pablo Zabaleta is injured. Micah will play on Sunday."
Sporting defender Xandao's flick gave the Portuguese side a one-goal lead to take to the Etihad Stadium next week, but after several spurned opportunities, Mancini feels his side were unlucky to lose.
"It wasn't a surprise because anything can happen in football, but I don't think we deserved to lose," said Mancini.
"We didn't play very well. But we still have a big chance. I am not worried. We will go through in the Europa League and Sunday will be a different game."
"I think that every game is difficult and different. We try to play good football. Sometimes we win, sometimes we lose."
City are favourites for the Europa League this season after dropping into the competition following their failure to qualify from their Champions League group, which included Napoli and Bayern Munich.
The club dispatched Porto in the last 32, 6-2 on aggregate, before Thursday's narrow loss to Sporting.