Silva complained of a tight hamstring in Manchester City's derby win over United on Monday, and has since been under intensive treatment, but he will be given as much time as possible to prove his fitness for the Wembley clash.
"We will decide on Sunday morning on David," Mancini said.
"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.
"He may be able to play some part, but we will make a final decision as late as possible."
He is unsure whether Monday's goal-scoring hero Sergio Aguero will be able to start, having come off the bench at Old Trafford to grab City's second-half winner.
He added: "I am happy because he had a good impact in the game on Monday night and it is important he didn't have any problems in his knee. Probably he is not 100 per cent but Sergio for us at 80 per cent is important."
Mancini also dismissed the possibility Chelsea will arrive at the game tired on the back of their Europa League defeat by Rubin Kazan on Thursday in Moscow.
"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," Mancini added.
"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."