Osayi-Samuel has one-year remaining on his contract with Fenerbahce, who are desperate to tie him down to a new deal.
Both parties are, however, yet to reach an agreement on the salary package.
The Nigeria international want an increase in his salary to commit his future to the club.
The Istanbul giants may be forced to sell the full-back instead of allowing him leave on a free transfer next summer.
Osayi-Samuel made 23 league appearances for the club last season.
He resume pre-season training with Fenerbahce under new coach, Jose Mourinho on Friday.
Olaitan Ibrahim