The Dutchman has returned to London after a post-Euro 2012 holiday and is to meet with Arsenal about his decision not to renew his contract at the Emirates
The Arsenal captain last week revealed that he will not renew his contract with the club, but Wenger and Gazidis want to speak to him without interference from his agent Kees Vos, to establish if there is any chance of keeping him in London until the end of his contract.
Manchester City are yet to formally announce their interest in adding 29-year-old Van Persie to their already strong squad, and it is believed they will not pay over-the-odds for a man with a poor injury record and with little resale value.
The Premier League champions are also looking to offload former Gunner Emmanuel Adebayor before launching any bid for the Dutchman and, as Goal.com exclusively revealed on Saturday, they are hoping to sell the Togo international to Tottenham for a bargain £5 million.
Although City have kept quiet on any pursuit of Van Persie, former Emirates favourite Kolo Toure and Mario Balotelli have declared they would like to see him join them in Manchester. It is also believed Nigel de Jong has been encouraging his international team-mate to join the Citizens.
Italian champions Juventus are also set to step up their efforts to capture the Gunners captain, and believe they stand a better chance than City as they are not a domestic rival.
Manchester United and Paris Saint-Germain are also keeping tabs on the situation, whilst club insiders are also wary of a potential bid from Jose Mourinho’s Real Madrid.
Meanwhile Wenger is also looking to ensure another transfer battle does not develop over forward Theo Walcott, who is out of contract at the end of next season. The England international is said to be a target for London rivals Chelsea.
In a week of bad news for Wenger, there has been a slight cause for a smile however with Arsenal fans giving the Frenchman a big vote of confidence.
The Arsenal Supporters Trust are set to reveal figures that 80 per cent of their members believe 62-year-old Wenger is doing a good job with the club, a dramatic rise from the previous campaign where 42% said he had taken the club as far as he could.