"At this point, I do expect he's headed to the market," Greiss' agent, Ray Petkau, told The Athletic's Pierre LeBrun on Monday.
But Petkau added that the pending unrestricted free agent "loves being a New York Islander" and would consider re-signing with the team if given the chance.
Greiss shared the crease with Semyon Varlamov this season but was ultimately relegated to a backup role. Greiss posted a .913 save percentage and 2.77 goals saved above average across 31 regular-season games before authoring a .929 save percentage in four playoff appearances.
The Islanders also boast a puck-stopper of the future in highly touted prospect Ilya Sorokin, who's expected to carve out a role after inking a pact through 2020-21 in July.
Greiss has been dependable in recent years, producing a .915 save percentage and 17.6 GSAA over five campaigns with New York.
The 34-year-old carried a $3.33-million cap hit in 2019-20, finishing off the three-year, $10-million contract he signed with the Islanders in January 2017.
The goalie market could include fellow pending UFAs Robin Lehner, Jacob Markstrom, Anton Khudobin, Corey Crawford, and Braden Holtby. It's also expected to feature Detroit Red Wings netminder Jimmy Howard, who said Sunday he's "probably not" re-signing with the club.