Conte is desperate to sign new players this January with the size of his squad a constant source of annoyance for the Italian.
Chiellini would be an excellent replacement for the exit-bound David Luiz, but the Serie A star seems intent on putting pen to paper on a new deal with Juventus.
He told Sky Italia: ‘Extend my contract with Juventus? I’ll meet the club after the holidays to discuss the contract extension and I think that there won’t be any surprise.
Chelsea 2017/18 Fixtures
Arsenal (A) – Wed Jan 3
Norwich City (A) – Sat Jan 6
Arsenal (A) – Wed Jan 10 (EFL Cup)
Leicester (H) – Sat Jan 13
Brighton (A) – Sat Jan 20
Arsenal (A) – Wed Jan 24 (EFL Cup)
Bournemouth (H) – Wed Jan 31
Watford (A) – Mon Jan 5
West Brom (H) – Mon Feb 12
Barcelona (H) – Tues Feb 20
Manchester United (A) – Sun Feb 25
‘Juventus feels like family to me and I couldn’t be better.’
Chelsea will still have the chance to convince Chiellini to join Conte in London until the 33-year-old inks a new contract.
Chiellini’s current deal at Juventus expires in the summer and the defender is free to speak to other clubs this January.
Crystal Palace attacker Wilfried Zaha, Porto star Alex Telles and Stoke goalkeeper Jack Butland are just a few players to be linked with a switch to Stamford Bridge this January as Conte targets adding some bulk to his squad.
The window has been open for barely a day, but Liverpool have already made a window-defining signing with the addition of Southampton defender Virgil van Dijk.
The centre-back reportedly turned down a move to Chelsea and Manchester City in favour of linking up with Jurgen Klopp at Liverpool, much to the disappointment of Conte.
More: Antonio Conte
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