According to The Daily Star, it is understood Van Persie has misgivings about some of Moyes' training methods.
The report said that former Everton boss Moyes now has his work cut out to convince Van Persie he is the right man for the United hotseat.
Despite starting the season brightly, with two goals in the champions'' first two games, the 30-year-old appeared out of sorts in the goalless draw with Chelsea and 1-0 defeat at Liverpool, the report added.
Van Persie cut a frustrated figure at Anfield on Sunday and looked close to losing his cool several times, the report further said.
A friend of Van Persie said that the player was not happy and therefore, he could not hide it on the pitch, adding that when he became frustrated, he was capable of doing something silly.