Fulham see Tillman as a replacement for Harry Wilson.
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The Wales midfielder is off contract at the end of the season and is set to depart.
The Daily Mail says USA midfielder Tillman is seen at Fulham as a readymade replacement, though will have to cough up to land the 23 year-old.
Tillman has a deal with Bayer to 2030 and could be rated at beyond €50m by the Germans.