Dewsbury-Hall, 26, is likely to leave Stamford Bridge after just one year, having followed manager Enzo Maresca from Leicester.
Despite struggling for playing time, Dewsbury-Hall had a good season, scoring five goals and providing three assists in 36 games across all competitions.
Fulham has initiated talks with Chelsea about a possible transfer, but the club has set a higher asking price, exceeding the £30 million they spent to sign Dewsbury-Hall.
West Ham has also expressed interest in the midfielder, having made an inquiry earlier in the summer, although they have not yet followed up.
