While the tweet only goes as far as saying that the Istanbul club are holding "transfer talks" with the 31-year-old, it is widely believed that a £4.7m move is imminent.
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It's still a significant act as it's the first sign from either of the clubs involved that a move for the prolific centre-forward has been discussed.
It's believed that the former Feyenoord man will fly to Turkey on Sunday and be presented to the fans on Monday, in what is likely to be a rapturous welcome.
The 31-year-old scored 30 goals for United as they won the league in 2012-13 following his £24million move from Arsenal.
Image credit: Eurosport
His impact since then has been muted due to a series of niggling injuries since then, and he was limited to 10 goals in 29 appearances under compatriot Louis van Gaal last season.
Fenerbahce signed Van Persie's former United team-mate Nani on Monday for a reported £4.25million.
If Van Persie is sold, United would have only Wayne Rooney, James Wilson and the injured Javier Hernandez, out with a broken collarbone, in their squad as recognised strikers following the exit of on-loan Falcao at the end of the season.
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