Antonio Conte wants a reunion with the striker who he managed while at Serie A giants Juventus.
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Swansea striker Fernando Llorente is wanted by Chelsea
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Fernando Llorente has scored six goals for Swansea
He could provide competition for Michy Batshuayi, who has struggled since joining from Marseille.
However, the South Wales Evening Post say the Blues are yet to make contact over a January deal.
It is claimed that Swansea chiefs have not received any offers or enquiries over their star asset.
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Antonio Conte and Fernando Llorente worked together at Juventus
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They also say that new manager Paul Clement is determined to keep Llorente at the Liberty Stadium.
The Swans are low in firepower with just Borja Baston - scorer of one goal from his first 11 league appearances - and Oli McBurnie in reserve.
Batshuayi will be handed a chance to impress Conte in Sunday's FA Cup clash with Peterborough.
Conte confirmed the Belgium international and Kurt Zouma will feature against the League One side.