The Sun says Fulham want to take Dewsbury-Hall on an initial loan for the new season.
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The former Leicester City midfielder is available from Chelsea this summer as they seek to cut squad numbers.
Dewsbury-Hall left the Foxes for Chelsea only a year ago for £30m.
Along with Dewsbury-Hall, Fulham are also in talks with Arsenal for winger Reiss Nelson, who spent last season on-loan.