The Dutch ace met with his agent Kees Vos after he was left out of the last two Manchester United line-ups, according to The Sun.
And Red Devils boss Louis van Gaal is set to hold talks with the 31-year-old next week.
Asked of Van Persie's future yesterday, Van Gaal said: You have to wait and see."
Turkis sides Fenerbahce and Galatasaray are both considering a move for the Dutch ace.
Van Persie is currently on a £220,000-a-week deal at United, but the suitors are both willing to extend that deal by three years.
And while The Sun say he had been ready to reject such an offer, recent events at United have made him reconsider.
Van Persie has scored 48 goals in 86 appearances for United since his £22m move from Arsenal in 2012.
However, his starting place under Van Gaal has come under threat after a poor season.
He has found the back of the net just 10 times this term.