Arsenal, on Friday, had rejected bids from Manchester United, Manchester City and Juventus. Reports suggest that United had made an offer worth £8 million while City and Juve made bids worth £12-14million for the 28-year old striker.
However, the Gunners are reluctant to sell their priced captain for anything less than £20million.
Meanwhile, boss Wenger is hopeful his captain will stay at the Emirates and pointed out fitness reasons for his absence from the pre-season tour.
"For me, Van Persie is one of the best strikers in the world, if not the best, and my desire is to keep him at the club. As for the rest, I will do what is in the best interests of Arsenal Football Club. That, at the moment, is where we are. There is not a lot more to say than that," Wenger was quoted as saying in ESPNsoccernet.
Arsenal lost two key players Cesc Fabregas and Samir Nasri late in the summer transfer window last season but Wenger is eager to avoid any such transfers this time around and is hopeful Van Persie would see through his 12-month contract.
"Robin was an exceptional leader last year, but we know how much we had to fight to come third because we missed out the start of the season. After seven games we had lost four and we have learned that for us it is vital for us to focus on the start of the season rather than on any transfers," Wenger said.
Arsenal have already signed two strikers Oliver Giroud from Montpellier and Germany star Lukas Podolski. Wenger said Arsenal are willing to sign more players but that depends on how many depart.
"We are still looking to add one or two players but it depends also on how many go out because we have to respect the squad number. It's important to respect that, so before we get players in we have to get some players out. That has not happened yet. The market is very quiet, he said.