Fabregas played alongside Van Persie at Arsenal earlier in his career and has been linked this summer with a move from Barcelona to United, where he would be reunited with the Dutchman.
United are understood to have submitted a bid of around £25million for the Spaniard last week, although Barca insist he is not for sale.
An improved offer of £30million is reported to have been tabled, and Van Persie is hopoing an agreement can be reached.
When asked if he would welcome Fabregas next season, Van Persie told reporters in Australia: "Of course, he's a great player."
Van Persie was speaking after United's 5-1 pre-season victory over the A-League Al Stars, when he netted the final goal of the game.