The 26-year-old is likely to leave Stamford Bridge this summer, just one year after following manager Enzo Maresca from Leicester.
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Dewsbury-Hall had a fine season despite struggling for minutes, scoring five goals and providing three assists in his 36 games across all competitions.
According to Ben Jacobs, Fulham have initiated talks with Chelsea over a move, but the Blues have told them they will have to pay more than the £30 million they spent to sign him.
West Ham are also interested in the midfielder having made an enquiry earlier in the summer, although they are yet to follow-up.