The 21-year-old Italy international, who is under contract at the Serie A side until 2022, could cost the Blues as much as £45m.
Fabregas is understood to be holding talks with Monaco ahead of a move to the Ligue 1 side, and bade a tearful farewell to Stamford Bridge after Chelsea’s FA Cup win over Nottingham Forest on Saturday.
Head coach Maurizio Sarri said last month he wants the club to buy another midfielder should Fabregas leave, saying:
“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.”
Barella broke into the Italy squad this season, and has won four caps after making his debut in October.