The Cottagers see Soyuncu as a replacement for Tosin Adarabioyo, who is leaving as a Bosman transfer this summer.
Soyuncu is available after spending time on-loan with Fenerbahce from Atletico Madrid. He left Leicester City last year.
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Atletico would prefer to sell outright but Fulham may find they would do a loan with a view to a permanent deal, says The Sun.
For his part, Soyuncu would be happy to return to England this summer.