Van Persie has been in and out of the United team because of injuries and is thought by some of his team-mates to be unhappy at Old Trafford.
Moyes has persistently defended the 30-year-old in public and denied suggestions of problems between the two.
However, Sportsmail understands the United manager has recently expressed private frustrations about Van Persie and is beginning to wonder if last season’s top scorer can be relied upon in the long term.
Van Persie’s goal record this season is good but his partnership with Wayne Rooney reached a new low when the duo hardly passed to each other in the Champions League defeat at Olympiacos.
Moyes was not bothered about Van Persie’s remarks concerning team shape in the wake of last week’s loss in Greece but is concerned about his form and body language on the pitch.
It is understood Moyes was beginning to wonder about Van Persie even before that game and it remains to be seen if the former Arsenal player manages to raise his levels between now and the end of the season.
United sources underlined just last week that Van Persie would not be sold this summer, even if he asked to leave.
However it will be up to Moyes to decide whether he remains the type of player to build a team around.
Van Persie is not the only player giving Moyes concern. He has privately bemoaned the fact that the core of the United squad is just not as good as he thought it was when he arrived from Everton to replace Sir Alex Ferguson.
-Daily Mail online