Van Persie has been in and out of the United team this season, often struggling with injuries, while some of his teammates consider him to be unhappy at Old Trafford.
The striker is also a doubt for Saturday’s clash with West Brom, after being taken ill while on international duty with Holland.
Moyes has continued to defend the 30-year-old in public, and has denied there is any problem between the two.
However, reports suggest the United manager has privately expressed his concern about van Persie, and is wondering whether last season’s top scorer can be relied upon in the long term.
Moyes was not bothered about van Persie’s comments in the aftermath of the Champions League defeat to Olympiakos, where the Dutch forward claimed his teammates were often occupying spaces he wanted to be in.
However, the Scot is concerned about his overall form and body language when on the pitch.
The final decision on whether van Persie remains at the club and is the sort of player to build a team around will rest with Moyes, who will be closely monitoring his form between now and the end of the season.