The 31-year-old has played just five Premier League games this season, with most of his appearances for the Blues coming in cup competitions. Fabregas's contract at Stamford Bridge expires in the summer and as a result, he could leave the club after five seasons.
Milan boss Gattuso has repeatedly stated his interest in the World Cup winner, but believes that Financial Fair Play restrictions could stop the club bringing the midfielder to Italy.
"We have stakes. We cannot do what we want," Gattuso told DAZN. "The club has been clear. Fabregas? There are important figures involved."
Although he has not signed a new deal at Chelsea, manager Maurizio Sarri would like Fabregas to stay at the club beyond the January transfer window.
"In this position we have only two players, Jorginho and Fabregas, so for me it would be really a problem without Cesc," Sarri said.
"I want him to stay, I don't know the final decision of Cesc and the club of course.
"But for me it's very important and if Cesc will go I think that we need to buy another player, and it's not easy because, technically, Cesc is a very important player.
"And I think that in the market it's very difficult to find a player with his characteristics."
Chelsea's policy is to only offer one-year contracts to players over 30, which could prove a stumbling block in Sarri's plan to retain the midfielder. Fabregas will be allowed to sign a pre-contract with another club in January, securing a transfer for the 2019-20 season.
In November, Fabregas denied that Milan had made an approach, but indicated that he would consider any offers which may come in January.
"I haven't spoken to anyone," Fabregas told reporters. "Obviously, in January I can sign with whoever I want and probably this will attract many clubs. But, so far, from what I can say right now, yes I will stay here until the end of the season."