Chelsea are interested in 20-year-old French sensation Dembele, who has hit 20 goals for Celtic this season.
And according to French news outlet SFR Sport, Chelsea have now made a bid for Dembele.
Celtic want £40m for the forward, who they signed on a free transfer from Fulham last summer.
Chelsea have reportedly launched a bid for Moussa Dembele
Antonio Conte is yet to make any signings this month
Chelsea boss Antonio Conte has yet to make any signings in January, but wants a striker before tomorrow’s 11pm deadline.
And Conte has money to spend with the Blues banking £60m from the sale of Oscar to Chinese Super League side Shanghai SIPG.
He also allowed John Obi Mikel to head to China with Tianjin TEDA while Patrick Bamford has joined Middlesbrough for £6m.
— Sara Menai (@SaraMenai) January 30, 2017
Premier League Done Deals: Every transfer out during January 2017
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Express Sport brings you up to date with every departure from the Premier League during the January transfer window
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Branislav Ivanovic is close to leaving Chelsea
Chelsea defender Branislav Ivanovic and goalkeeper Asmir Begovic could also leave before the window shuts.
On Ivanovic, Conte today said: "I know he's talking to other clubs but I don't know (about a decision).
"It's important to respect the decision of the player, above all if he's a legend of the club. I have great respect."
And when pressed on Begovic, Conte added: "Until now I haven't any news about Asmir.”