The Sun says Sir Alex Ferguson is aware the £20million-rated striker is yet to commit to a new contract at The Emirates.
And the United chief's interest has intensified after Van Persie admitted prizes mean more to him than money.
He recently admitted: "In the last four years I've won only one prize, the FA Cup, and that is too little. I want more."
Van Persie has one year left on his current deal.
A Dutch source added: "Robin loves it at Arsenal but he is getting to the age when he wants to win things. He knows that there are clubs interested in him and is waiting to see what happens."
Van Persie signed for Arsenal five years ago but injuries have restricted him to 79 League starts.