Van Persie announced six weeks ago that he was determined to leave the Gunners, but despite strong interest from United, City and Juventus, the 29-year-old remains an Arsenal player.
Arsenal rejected a bid from Manchester United for the striker three weeks ago and although the London club appear to have reduced their asking price to ?20million, van Persie still has not secured the move to Old Trafford that he is understood to want.
While confusion surrounds the striker's future, what is clear is that his suitors value him highly.
Old Trafford appears to be van Persie's preferred destination, but Manchester City captain Vincent Kompany would love to see van Persie, who scored a staggering 37 goals last season, move to the Etihad Stadium.
"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 a section of the travelling support when he came off the bench, but Arsenal centre-back Thomas Vermaelen is still confident his captain will stay.
"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."
Van Persie cited Arsenal's supposed lack of ambition as one of his reasons for wanting to leave, but the London club have been busy in the transfer market this summer, signing Olivier Giroud, Lukas Podolski and Santiago Cazorla.
Arsenal's other centre-half, Laurent Koscielny, believes Giroud will provide Arsenal with some firepower that will be required if van Persie departs.
"I played with him at Tours and he was a great player then - now he is even more confident and scores a lot of goals," Koscielny told Arsenal Player.
"I know his qualities and he will give a lot for us.
"I know he has the physical quality to play in this league. For a striker it is [about] confidence and I am sure he is working hard to start well with Arsenal.
"He is tall, like Marouane Chamakh and is also good with his back to goal. I think if we play with technical guys he will be happy, and in the box he is a good finisher."
Alex Song, meanwhile, has his heart set on a move to Barcelona, according to his international colleague Carlos Kameni.
Arsenal boss Arsene Wenger insists claims Song wants to move to the Nou Camp have no foundation, but Malaga goalkeeper Kameni thinks otherwise.
"We were together on holiday and he said he wants to go to Barcelona," Kameni told Portuguese newspaper Abola.
"Everyone wants to play for Barcelona. Song would fit right in at Barcelona. He has all the qualities to play there.
"He is like Yaya Toure, but with more responsibility. He's doing well. He works hard and is the complete player."
