Davis has been a target of Middlesbrough and Everton all summer with Fulham refusing to sell the midfielder.
A statement on the official Fulham website reads: "The Club is disappointed to announce that this morning, Sean Davis handed in a written transfer request to Chris Coleman citing his ambition to 'further his career' as his reason to want to leave Fulham.
Chris is obviously saddened by the request as he believes that Sean had a huge future at the Club and that his career prospects would have been considerably enhanced playing for Fulham in a pivotal role.
The Club is now considering its options in light of this news and will of course keep all fans informed of any progress."