The 26-year-old has been heavily linked with a transfer to Old Trafford in recent weeks and the Red Devils had a bid of around £26m rejected by Barcelona earlier this month.
Van Persie played alongside Fàbregas for most of his Arsenal career before the Spaniard moved back to his boyhood club in August 2011.
And when asked whether he would like to be reunited with Fàbregas at Old Trafford, Van Persie replied: “Of course, he’s a great player.”
Barcelona have insisted that the playmaker is not for sale this summer, despite David Moyes’ pursuit of the former Gunners captain.
Speaking earlier this week, the Scot confirmed that he is aiming to bolster his midfield options ahead of the new campaign.
Moyes said: “When I got the job, I was made aware of what could possibly be done to improve things, and signing a midfield player was one that we thought we could possibly add to the squad.
“At the moment that’s probably our priority – to try and add a player in that position.”