The skipper's current deal at the Emirates Stadium expires at the end of next season and no plans have yet been arranged for talks over an extension.
Speaking in March, manager Arsene Wenger said: "I am confident [he will stay] for two reasons. First of all I want to convince him to stay here and to extend his contract.
"Secondly he is not free at the end of this season - he has one year of his contract left anyway."
However, rather than hold discussions with the club in between the end of the season and his European Championship campaign with Holland as originally suggested, Van Persie could postpone the talks further, according to BBC Sport.