Spain international Silva has been struggling with a hamstring injury sustained in City's 2-1 victory over rivals Manchester United at Old Trafford on Monday.
The win cut the gap at the top of the English Premier League to 12 points but with the title effectively lost, City have a chance to salvage their season by making the FA Cup final.
Mancini confirmed that he will give Silva every chance to play a part in the match at Wembley on Sunday.
"We will decide on the day of the game (whether he will play). We don't know if it is possible but if there is a risk, he doesn't play," said Mancini.
"It (Silva's injury) is getting better. Yesterday he ran. I think we have a chance. I don't think he can play 100 per cent but it is important he is close."
Mancini said he did not expect Chelsea to show any signs of tiredness, despite having just returned from Russia for a Europa League quarter-final with Rubin Kazan.
"Every game against Chelsea is difficult. They are a good team in their best moment this season, doing very well and I am happy for Rafael Benitez because he is a good manager," Mancini said.
"This game is important. It will be different from the other game we played against Chelsea. It is more difficult, they are in a good moment.
"They played against Rubin Kazan with three or four players they will play against us. I think they rested five or six players."
Manchester City last won the FA Cup in 2011 and Mancini said he was looking forward to heading to the landmark London stadium for the semi-final.
"I think to play at Wembley is fantastic. For the FA Cup or the Premier League, for all the supporters there is a magic moment," added Mancini.
"Every trophy is important for every team. For us, more so, because we have this chance to go to the final.
"I think it was important for the next game that we have the FA Cup. The Premier League championship is not important now, it is finished now."
Mancini has also restated his desire to see the Premier League have a mid-season break in light of the hectic schedules some of his squad will face even when the season comes to an end.
"I think that in England you need to have a break in December for the national team because we play a lot of games," added the Italian.
"The moment that they decide to give players one week off in December it will be good for the teams and national team.
"It is incredible. These players don't have the time to recover very well. When we finish the Premier League games, we go one week in New York and after they come back some players play in the Confederations Cup and qualification for World Cup. That is incredible."