Bogdan Lobont is the current number one at the Amsterdam ArenA and he is expected to be pushed hard by rising star Maarten Stekelenburg next season.
This scenario would suggest Boschker, who has a deal which runs until 2005, will be third choice next term.
Boschker, 33, has insisted he will not accept the situation and will look to move on.
"I want to be in the first 18 players for games regularly," Boschker told De Telegraaf. "With Lobont and Stekelenburg, that's difficult and maybe it's better to leave."
It would appear as if a decision will be made in the near future, as Boschker has an offer on the table from De Graafschap.
"I have got a week's thinking time," he said. "There's concrete interest from De Graafschap."
Ajax coach Ronald Koeman is said to be ready to let the former Twente man move on, with Hans Vonk a possible replacement.
Stekelenburg is rated highly at Ajax, but the 21-year-old may not be handed a starting berth next term - instead being loaned out to another Eredivisie club.
This would leave Koeman short of cover and the free transfer capture of South African Vonk from Heerenveen would suit all parties.
