AC Milan are keen to sign Fabregas in January and the Blues have looked at Barca's disgruntled Suarez.
Chelsea boss, Maurizio Sarri does not want the 31-year-old to go, but the Spaniard wants more football than he is getting at the moment.
Sarri has told the club's board that he does not want Fabregas to go until a direct replacement has been sorted out as he is his only true cover for Jorginho.
However, Fabregas has made only four Premier League appearances this season, starting only in the recent defeat away to Wolves.
Suarez wants to leave Barcelona after making only one substitute appearance in La Liga this season, and would cost around £15million.
The Blues value Fabregas at around £11m.
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