The Spaniard felt his hamstring tighten in Monday's 2-1 victory over Premier League leaders Manchester United at Old Trafford.
"We don't know if it's possible for him to play or whether it might be a risk if he does. He has a chance, but I don't think he can recover fully," manager Roberto Mancini said on the club's website on Friday.
"He may be able to play some part, but we will make a final decision as late as possible... we will decide on Sunday morning."
City travel to Wembley to face a Chelsea side who will have had much less rest after Rafael Benitez's side played in the Europa League in Russia on Thursday, reaching the semi-finals with a 5-4 aggregate win over Rubin Kazan.
Despite this, Mancini reckoned fatigue would not be a factor for the London side.
"They will probably have three or four of the team that started the Europa League game but they rested the five or six players so they won't be tired," the Italian, who guided City to FA Cup glory in 2011, said.
"Chelsea will be difficult and they are playing well at the moment so we know we will have to play our best to win this game.
"We are looking forward to the challenge and to playing at Wembley. This is a very important competition for us and we want to win it."
