The Gunners are aiming to receive around £25-£30million for the Dutch forward and the bids have been deemed not good enough.
The Netherlands international confirmed he was leaving Arsenal earlier this month with his contract expiring next summer.
Van Persie has been left out of the Gunners squad for their pre-season tour of Asia as the club are hoping to sell him before the season starts next month.
He was named both the Professional Footballers' Association and Football Writers' player of the year last season and finished as Premier League top goalscorer.
Source: DSG
