The 49-year-old United coach has briefly stepped into Mike Phelan's position as assistant manager while he recovers from a knee operation, and he's backed his fellow Dutchman to pursue management in the future.
Van Persie has worked with the club's youngsters at the Carrington training gourd, and Meulensteen has been left impressed by his work.
Speaking to Algemeen Dagblad, Meulensteen said: "When you see how he works with the youngsters, he's committed, patient.
"There is a coach hiding inside him, although I think he will play as long as he can."
Van Persie has fired United to the top of the Premier League table, and victory over Aston Villa tonight can clinch a 13th league title.
And Meulensteen insists it's Van Persie's attitude and commitment to improvement that's allowed him to slot seamlessly into the United squad.
"Robin loves the game," Meulensteen continued. "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."
Paul Scholes and Ryan Giggs are two United legends slightly further along in their careers who are expected to make the jump from pitch to dugout once they retire. And it seems Van Persie could follow them too.