The defender could leave Atletico Madrid before the end of the transfer window just six months after joining the club.
Soyuncu completed a free transfer to the Spanish giants in the summer following five years at Leicester.
Despite signing a four-year deal through to 2027, the 27-year-old has made just one league start for Atletico this season.
He is now being linked with a January loan move and is even attracting Premier League interest.
According to A Bola, Fulham are one of three clubs currently interested in Soyuncu.
The Cottagers are said to be facing competition from Porto and Roma for his signature, though.
Fenerbahce have also made a move for Soyuncu, the report adds, but were rejected by the player.
However, Atletico are understood to be open to a loan deal before the window closes.
The Turkish international has made just nine appearances for the club across all competitions this season.
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Of those, just two have come from the start, with his solitary La Liga start ending after 45 minutes.
Soyuncu was withdrawn at half-time in a 2-0 loss to Athletic Bilbao in December.
During five years in England, the defender scored four goals in 98 appearances for Leicester.
He was also part of the Foxes’ FA Cup-winning side in 2021 and played for the club in Europe.
