The Switzerland international scored three times in three games during Euro 2008, and the attacker is about to join the eighth club of his career.
The Cottagers have reportedly approached Yakin, who could come as a free agent, and a Qatari club are also keen on the former Galatasaray star.
"For the moment he's with us, part of our squad, and I don't know where he's going to move," Young Boys spokesman Charles Beuret told setantasports.com.
"Yakin has an option to leave the club this summer.
"He told us he's leaving the club and it's up to him and to his family to find the best option for his future."
Fulham boss Hodgson knows all about Yakin from his time as coach of Grasshoppers.