With just days to go until the start of the new season, Arsenal's reported ?20 million asking price for the striker, who scored a mammoth 37 goals last term, has yet to be met.
Manchester United appear to be leading the chasing pack for the Gunners captain but City skipper Kompany said the 29-year-old van Persie would be more than welcome at Eastlands.
"It's very easy to say you want to play next to Robin van Persie," Kompany told Sky Sports News.
"He's a great player. He's proved it so many times last season and any team he would play for he'd make it stronger."
Van Persie made his only pre-season appearance for Arsenal on Sunday against Cologne.
The Dutchman, whose contract expires at the end of the 2012-13 season, was booed by some Gunners fans when he came off the bench, but Arsenal centre-back Thomas Vermaelen was optimistic the star striker would stay with the north London club.
"To me he looks fit and sharp in training," Vermaelen said.
"He's working hard. He's working on his fitness. I don't see anything (different) and I hope he stays the next four years as well.
"I don't know what happens behind the scenes but at the moment I can only say he's a player for Arsenal.
"I feel really positive for the new season. If we all stay fit, the squad is strong enough to compete for the title."
Source: AFP
Source: AFP