It is understood that the European champions were sounded out recently by parties representing the Dutchman about their interest in making a move for the striker, whose contract expires in 12 months’ time.
But Barcelona made it clear they do not want to make a move for Van Persie despite a sensational campaign in which he scored 37 goals for Arsenal in all competitions, including 30 in the Premier League.
It is believed that the combination of Van Persie’s age – he turns 29 in August – and the expense of a £20 million transfer fee plus expected £10m-a-year salary have put off the Spanish giants, who are trying to cut their debts and rein in costs.
Goal.com revealed on Wednesday that Juventus have pulled out of the race to sign the Dutchman because of his £200,000-a-week salary demands, which leaves Manchester City as the clear frontrunners to capture Van Persie if Arsenal sanction a summer transfer.
The 28-year-old and his agent Kees Vos opened contract talks with Arsene Wenger and Gunners chief executive Ivan Gazidis on Wednesday before Van Persie flew out from England on Thursday to link up with the Netherlands squad as they begin their Euro 2012 preparations.
Wenger had said that he expected the future of his captain and star player to be resolved before Van Persie joined up with his national squad but the Dutchman’s future remains shrouded in doubt.
Sources close to the negotiations have said that nothing was resolved by the end of Wednesday's round of talks, which took place in London. Discussions are said to be "ongoing" and further talks are due to take place in the coming weeks.
Arsenal fear the spending power of Europe’s richest clubs have turned Van Persie’s head but are adamant they would rather let him go on a free next year than sell him for around £20m this summer.
Real Madrid have yet to make a move for the Dutchman, whose principal admirers are new Premier League champions City.
Vos admitted to Goal.com on Monday that he was a guest of Brian Marwood, Manchester City’s highest ranking football executive, at an Etihad Stadium match “three months ago” although he denied that the meeting was to discuss a possible transfer for his superstar client.
Roberto Mancini spoke earlier this year of his admiration for Van Persie and is targeting an A-list centre forward in the forthcoming transfer window, with City ready to off-load Carlos Tevez and Edin Dzeko.
However, it is believed that the City manager does not want a repeat of the Samir Nasri saga last summer, which dragged on into the new season before it was resolved.
Mancini wants his principal targets to be captured in time for City’s pre-season programme, which begins in the second week of July and will turn his attention elsewhere if Van Persie is not signed by them.