Fabregas left for Monaco after four and a half years at the club and Sarri has asked the club to sign a replacement.
Chelsea are understood to be keen on signing Nicolo Barella, 21, from Cagliari and Zenit Saint Petersburg star Leandro Paredes, 24.
However, Sarri is hoping youngster Ampadu, 18, can emulate Callum Hudson-Odoi, 18, by making the leap into the first team.
“I hope the same for [Ethan] Ampadu,” the Italian said.
“Of course, playing as a central midfielder in our team is not easy.
“We need to try and try and try in training, but I think that he is able to do it.
“In the future maybe he can step up, but we have to work.
“The player who plays in that position usually touches about 120, 130 balls [per game], so I think we need a specialist there.”
Welsh international Ampadu is yet to make an appearance in the Premier League this season – his only action coming in the League Cup and the FA Cup.
Meanwhile, Hudson-Odoi is beginning to make the step up after initially struggling to force his way into Sarri’s plans.
The winger made his second league appearance of the current campaign as a substitute against Newcastle.
However, he is said to be frustrated by a lack of action and is reportedly keen on moving to Bayern Munich, who have made four separate bids to sign him in the January transfer window.
The latest bid is said to be in the region of £35million and reports that emerged over the weekend claim he has asked the club to accept it to so he can move on.
But Sarri is keen to keep him and urged him to stay and fight for his place.
“He is very young, and he has a very great future here in England with the national team and with Chelsea. To stay here is better for him,” he said last week.
“He is ready I think for the big games. Of course we have very important players in the same position.
“Do people want Willian on the bench? Or Pedro? I can play with only two wingers.
“Three is difficult – but now he is ready. He can play.
“Of course sometimes he will be on the bench but that is the same as others. I can start to consider him on the same level.”