The Dutch star wants to start in the Champions League play-off return leg against Shakhtar Donetsk next week.
Van Persie has yet to make a start for his new club due to lacking match fitness but did make an appearance in the goalless draw against Shakhtar Donetsk in the Champions League play-of preliminary round first-leg tie in Istanbul.
The 31-year-old striker played the last 20 minutes against Shakhtar but was unable to get his name on the scoresheet.
Van Persie featured in the latest BT Sport advert for the Champions League but still has another play-off round to progress past even if his side knock Shakhtar out of the competition.
Fenerbahçe could go onto face United in the Champions League play-off stages if they find a way past Shakhtar in Ukraine.
Van Persie joined by another former United teammate after signing a three-year deal with the Yellow Canaries. Luis Nani had already completed his move from Old Trafford to Fenerbahçe the week before.
Fenerbahçe finished last season as runners-up and are currently managed by former Olympiakos boss Vitor Pereira.