The Netherlands international participated in training today at the Can Bartu training grounds.
Fanatik initially reported that Van Persie could be out for up to a month with injury.
However, the Dutch star has made a recovery sooner than expected and could be ready to make his league debut against Eskişehirspor.
Van Persie already made his debut for his new side in the goalless draw against Shakhtar Donetsk in the Champions League play-off preliminary first-leg game.
The 32-year-old striker did however, miss the return leg with injury.
The experienced striker had an ankle injury in all but one season (2007) and only managed a league campaign without significant time on the sidelines for Manchester United – he won the league title the same season.
The Netherlands international joined Fenerbahçe on £3.8 million move from United last month.
The Fenerbahçe team was rocked by a shooting incident today. Mehmet Topal’s car was shot at after training but the bulletproof window of his Mercedes G 96 prevented injury to himself and his passenger Uygar Mert Zeybek.