Netherlands international Van Persie, who turns 29 at the start of August, announced after EURO 2012 he would not be renewing his current Arsenal deal, which expires at the end of next season.
However, despite reported interest from Manchester City and Juventus, both willing to offer the Dutchman big wages, Van Persie has joined up with his team-mates at their Hertfordshire base after an extended break.
After Van Persie made a carefully-worded announcement on Facebook, which included questioning the club's ambitions, Arsenal responded by saying while it 'respected' its captain's position and it was 'confident he will fulfil his commitments to the club'.
Those would include jetting off with the rest of the squad for the start of Arsenal's Asia tour, where the Gunners will play a Malaysia XI at the National Stadium in Bukit Jalil, Kuala Lumpur at the start of next week and is followed by a friendly against Premier League champion Manchester City at Beijing's Bird's Nest stadium on 27 July.
Wenger has already moved to bolster Arsenal's frontline next season with the purchase of France striker Olivier Giroud and German international Lukas Podolski.
Further additions are also expected, regardless of Van Persie's future - with Rennes midfielder Yann M'Vila, Barcelona's Ibrahim Afellay and Corinthians midfielder Paulinho all reported targets.
However, Arsenal will also look to sell off fringe players.
The club confirmed Mexico forward Carlos Vela is in talks with Real Sociedad to formalise a permanent move after his loan spell last season.
Other players who could also be allowed to move on include striker Nicklas Bendtner and Russian Andrey Arshavin, both who were also away from the Gunners on loan last season.
Arsenal found some form towards the end of the previous campaign, when fired by the goals of Van Persie, it edged back into the top four to secure third place and with it automatic UEFA Champions League qualification again.
Winger Alex Oxlade-Chamberlain cannot wait for the new campaign to get under way, when the Gunners will again be out to silence their critics.
The England international told Arsenal Player: "To get back into training, see the boys and play football again - I just can't wait for it.
"I spoke to the boss and physio, and they said I am in on Thursday, but I asked if I could come in earlier.
"I just can't wait to get started again and get cracking with the new season."