
The midfielder has struggled for regular game-time at Stamford Bridge this season under Antonio Conte.
The Italian has set up with summer signing N'Golo Kante and Nemanja Matic in the middle.
Fabregas has still made an impact when involved but has only started five Premier League games.
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Cesc Fabregas wants to stay at Chelsea beyond January
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Antonio Conte's Chelsea lead the Premier League by eight points
There is interest from Serie A but, according to Sky Sports, Fabregas is determined to stay in west London.
Fabregas joined Chelsea from Barcelona and helped them win the title in his first season.
But he struggled last season and is now out of favour.
Most valuable Chelsea players
Mon, January 16, 2017
Click through the gallery to reveal the five most valuable Chelsea players according to CIES Football Observatory stats
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Click through the gallery to reveal the five most valuable Chelsea players according to CIES Football Observatory stats
Conte is expected to bolster his midfield and is lining up a move for Franck Kessie and has been linked with Arturo Vidal – putting Fabregas' future further in doubt.
And the Spain star recently admitted he was sad sitting on the bench.
"I play football to win and enjoy,” he said.
“When I don’t play I’m sad and I don’t enjoy it but I’m happy the team is doing well. Football is my life, it’s everything to me.
“Every time I’m on the pitch I try to do my best. In this game it went well again so I just need to keep going and show the manager I deserve to play."
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