The statement read: “Everyone at the club would like to wish Robin well for the future as he links up again with Nani, who also joined Fenerbahce recently.”
Nani and Van Persie signed for Fenerbahçe in July with both players signing a three-year deal with the Turkish giants.
The Portuguese international joined on a £4.3 million move while Van Persie was snapped up for £3.8 million.
Nani won four Premier League titles with United as well as the Champions League and World Club Cup over the course of eight seasons at the club.
Van Persie played a key role in the Red Devils winning their 20th league title in the 2012-13 league campaign.
The former United stars have both been included in the 24 man squad ahead of the Champions League preliminary play-off tie against Shakhtar Donetsk at the end of the month.
Fenerbahçe could end up facing United in the final play-off stages if they knock Shakhtar out of the competition.