But Celtic are extremely reluctant to sell Dembele before tomorrow night's 11pm deadline.
And the Scottish champions will not accept anything less than £40million for Dembele.
Chelsea are interested in a move for Celtic star Moussa Dembele
Chelsea have been looking to bring a striker to Stamford Bridge throughout the transfer window.
With Diego Costa’s future in doubt and Michy Batshuayi struggling to make an impact, Conte knows he needs more firepower.
Swansea’s Fernando Llorente has been heavily linked with a move but it now appears Chelsea have moved their interest on to Dembele.
Chelsea transfers: Deadline day ins and outs rumours rated
Mon, January 30, 2017
Football Whispers have rated Sunderland's chances in the transfer market ahead of deadline day (1 – unlikely, 5 – likely)
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Football Whispers have rated the likelihood of Chelsea transfer deals (out of 5)
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Moussa Dembele has 20 goals for Celtic this season
Dembele joined Celtic on a free transfer from Fulham last summer.
The Frenchman signed a four-year deal with Brendan Rodgers’ side.
The 20-year-old has since scored 20 goals in 38 appearances for the Hoops, including three in the Champions League group stages.