The Dutch pair worked closely together last season.
Meulensteen told BBC: "The first time I saw Robin van Persie when he came to the club, I said: 'Listen, you'll fit like a glove here. The way I know you from a distance, the way you play, the way I know Manchester United, how we want to play and the way we operate, I think you will absolutely love it'. He's done that.
"We were on the training pitch in the first week, I was setting up another possession game and I saw the manager speaking to Robin. I overheard him talking about the numbers that were available: 'There are only two numbers available, 20 and 21, what do you prefer?'. So to help Robin a little bit, I said: 'You can only be number 20 because if we do win the title that's number 20, which you will be carrying on your back'."