Meyer became a free agent at the end of last season after seeing out his contract with Schalke. However, the 22-year-old has had difficulty in finding a new club after demanding £77,000-per-week, German newspaper Bild reports.
Arsenal were the first club that were interested in Meyer but were told that the midfielder wanted more than £4m a year. This fee was deemed too high by Arsenal for a player who managed just one goal and one assist in 28 appearances last season, which led to his omission from the Germany squad for the World Cup.
Fenerbahce are now favourites to sign Meyer after initial hesitation, with the German's agent in talks with the club. The Turkish side are still reluctant to pay the wages Meyer wants, but are willing to offer a sign-on fee and bonuses.
During the contract stand-off between Meyer and Schalke, relations turned sour with the player accusing the club of bullying. Meyer was then suspended by the club after launching personal attacks against the manager, sporting director and chairman.