The Dutch bowed out of the tournament at the group stage and City boss Roberto Mancini is hoping to capitalise on that by making a formal bid for the 28-year-old.
Van Persie’s contract at the Emirates Stadium expires in 12-months and has yet to sign an extension despite holding talks with Gunners officials before jetting off to the championships in Poland and Ukraine.
Mancini is desperate to add a proven Premier League forward to his title winning squad with Van Persie fitting the mould and the Italian is eager to get his man after missing out on Eden Hazard to Chelsea and believes they are in a strong position to prise him away from North London.
He is also keen to avoid a similar scenario to last summer when they failed to land top target Alexis Sanchez before coming embroiled in a transfer saga with Arsenal over Samir Nasri.
With his contract having only a year to run City are prepared to pay just £20 million for the Van Persie man although may be forced to exceed that with Barcelona and Juventus also monitoring his situation.
The champions are looking to cut costs before making any additions and Mancini has been instructed by the clubs hierarchy to make getting rid of high earners Wayne Bridge, Emmanuel Adebayor and Roque Santa Cruz a priority.
Edin Dzeko is also likely to be sold to generate fundsafter falling out of favour at the Etihad Stadium with Bayern Munich reportedly keen to sign him just 18-months after joining the club for £27 million from Wolfsburg.
Mario Balotelli, however, looks likely to stay after he was linked with a move to AC Milan earlier this year.