It is unlikely that a final decision will be made before Van Persie links up with the Netherlands squad on Thursday.
The 28-year-old, who has a year left on his contract, ended the season with 41 goals in 53 games for club and country.
Of that tally, 37 came in 48 appearances for Arsenal and he was the Premier League's leading marksman with 30 goals in 38 matches.
A number of leading sides have registered interest in signing the Gunners captain, who was named Professional Footballers' Association and Football Writers' player of the year.
