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Cristante is on the books at Italian club Atalanta but could be on the move shortly.
Starsport understands Atalanta will turn his loan from Benfica into a permanent transfer for around £3.5m and then sell him on.
And Stamford Bridge looks like a likely destination for Cristante.
The 22-year-old started his career at AC Milan before moving on to Benfica.
He’s played on loan at Palermo and Pescara but it’s at current side Atalanta that he’s made the biggest impact.
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Manchester United are also said to be keen on Cristante, and a bidding war between the Old Trafford club and Chelsea could emerge.
Antonio Conte is after fresh faces in January as he bids challenge domestically and in Europe in the second-half of the season.
“If there is the possibility to improve the squad on the numerical aspect, I think it would be a good choice,” he said.
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“Bryan Cristante says Chelsea want to sign him”
“But, at the same time, I'm enjoying working with these players.
“At this moment, I'm ready to continue to play with all these players. They are showing me great commitment, great behaviours, and I'm very happy to work with these players.
“At the same time, if there is the possibility to improve our squad, I think the club will try to do this.”