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The 22-year-old France international's arrival at Stamford Bridge could bring about Nemanja Matić's departure.
Blues boss Antonio Conte, despite fielding the former Benfica man 35 times in the Premier League last season, clearly feels as though he needs an upgrade on Matić.
But is Bakayoko the man for the job? We've delved into the stats to see how the Frenchman's stats from last season compare to the two-time Premier League winner's.
Would selling Matić to United for £40million and bringing in Bakayoko for the same price be great business for Chelsea?
Or would the west Londoners be strengthening a rival while weakening their own options?