The 49-year-old, who has acted as Sir Alex Ferguson's No.2 while Mike Phelan recovers from a routine knee operation, expects Van Persie to put off the prospect of retirement for as long as possible.
Having witnessed the striker work with the club's young players on the training ground, however, Meulensteen believes he has the necessary qualities to take up coaching.
"When you see how he works with the youngsters, he's committed, patient," he told Algemeen Dagblad. "There is a coach hiding inside him, although I think he will play as long as he can."
The Netherlands international's compatriot revealed that Van Persie slotted into the United squad seamlessly after arriving from Arsenal last summer.
"Robin loves the game," Meulensteen explained. "I told him right after he came here: you here, it's a good fit. He immediately found his way in the group. No arrogance, nothing. Perfect."