Barella, 21, is regarded as an outstanding talent among his generation in Italy but is reluctant to move in January as his stock continues to rise in Serie A.
Napoli and Inter are willing to wait until June before entering the market for Barella, so it would take a persuasive offer from Chelsea to change his mind and lure him to the Premier League during the January window.
He has previously been compared to Steven Gerrard, and should he sign then he would compete with the likes of Mateo Kovacic, Ruben Loftus-Cheek and Ross Barkley for a starting berth under Maurzio Sarri.
Fabregas received an emotional send-off towards the end of Chelsea's 2-0 win over Nottingham Forest on Saturday having made 198 appearances for the west London outfit.
He will now reunite with former Arsenal team-mate and current Monaco manager Thierry Henry as he looks to help the 2016-17 champions navigate themselves to safety during the second half of the campaign.
Chelsea could look to sign a more direct replacement for Fabregas, as well as keeping Barella on their radar, as Sarri prepares to lose his back-up option for Jorginho.
Either way it is clear the former Napoli boss wishes to bolster his midfield before the window shuts at the end of the month.
"If Cesc goes, of course, we will need a replacement. Now with the midfielders we are in trouble I think.
"I don't know the [injury] situation of Loftus-Cheek, if it is serious or not. Without Cesc we have only five [midfielders] so we are in trouble. We need a replacement."
Chelsea are also on the hunt for a new striker during the window, with Alvaro Morata moving towards the exit door after his agent held talks with Sevilla regarding a loan move until the end of the season.