Dewsbury-Hall had a successful season despite limited playing time, scoring five goals and providing three assists in 36 games across all competitions.
Fulham has initiated talks with Chelsea regarding a potential transfer, but the Blues have indicated that they will require a higher price than the £30 million that was spent on Dewsbury-Hall.
West Ham has also expressed interest in the midfielder, having made an initial enquiry earlier in the summer, although they have yet to follow up.