Reports from various sources suggest that the Gunners have also turned down similar offers from Manchester City and Juventus.
The 28-year old Dutch international, who has 12 months left on his contract, refused to join his team-mates on Arsenal's pre-season tour of Asia and requested the club to sort out his future by Saturday, according to reports.
Arsenal are keen to hold on to their asking price believed to be in the region of £25-30milliion.
Reports also suggest that United's bid for the Dutch striker is way behind Arsenal's valuation (£20m). However, the former champions will not be ready to splash out any big money move for a player who turns 29 in August.
Arsenal, who recently revamped their strike force with the signing of French striker Oliver Giroud and German star Lukas Podolski, are ready to offload Van Persie if potential clubs are ready to meet the strikers' asking price.
The Dutch star scored 30 goals last season and recorded 41 goals in 53 games for club and country. The former Feyenoord striker was named PFA's and football Writers' player of the year last season.