Clasie spent last season on-loan with Feyenoord, though they decided against taking up their permanent option.
De Telegraaf says AZ are now in contact about a deal for the midfielder next term. AZ coach Arne Slot spoke with Clasie before the player left for his summer break.
Clasie does not want to return to England under any circumstances. He had hoped to stay with Feyenoord next season, but that option is now a non-starter.
Instead, AZ are now making a move and are hoping to convince Saints to release Clasie from the final year of his contract.