The Gunners captain declared earlier this week that he would not be renewing his contract with the club - which has just 12 months left to run.
Since his announcement a host of clubs have been linked, but Sky Sports understands that just three clubs are currently challenging for his signature - Juventus, Manchester City and Manchester United.
All three have been in the reckoning all summer and that has not changed.
Both City and United are set to offer him the chance to remain in England, should he leave the Emirates, but Juve are pushing hard with Italian sources claiming their offer would make him one of the highest players in Europe.
Van Persie has made it clear that silverware is the most important thing to him at this point - although all three clubs would be well in contention next season to challenge for every honour.
The player himself is currently on holiday and is due to return to England next week, when more talks with Arsenal are likely.
Paris Saint Germain have been linked, and whilst nobody could deny they could afford Van Persie, Sky Sports understands that the player would not entertain a move to the French capital at this point in his career.
And PSG chairman Nasser al-Khelaifi says his club have not made contact with the Dutch forward.
"We have never talked with Van Persie," he told l'Equipe.
"We trust our current forwards. But we are trying to find another one."
Various reports claim Real Madrid, Barcelona and AC Milan are also in contention but those reports are believed to be wide of the mark at present.
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