The 24-year-old's agent Rodger Linse says the Fulham midfielder would fit in "perfectly" at Stamford Bridge after reports of a £10m offer from the Champions League winner.
Dembele's current deal at Craven Cottage runs out at the end of next season and he is reportedly being chased by Chelsea and Manchester United over a possible £10 million transfer.
When asked about Chelsea's interest, Linse said: "It fits Mousa’s ambitions perfectly to become the replacement for someone like Frank Lampard one day, just as playing in the Champions League does as well."
The former AZ Alkmaar player moved to Craven Cottage from Holland in 2010 and could now make the short trip to Fulham's local rival at Stamford Bridge.
Chelsea is also close to signing Dembele's countryman, Eden Hazard, as the club looks to rebuild its squad with Europe's top young talent.
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