The Frenchman lost his place at Leeds United last season and will leave Elland Road as a free agent.
The 26-year-old received no Premier League game time at all last season and opted not to extend his contract with the Whites.
Meslier joined Leeds United on loan from Lorient in 2019 before making the move permanent, going on to make 215 appearances for the club and keeping 72 clean sheets across the Championship and Premier League.
He helped Leeds win the Championship title twice during his time at Elland Road, establishing himself as the club's first-choice goalkeeper for several seasons.
Meslier is now searching for a new club and will be available on a free transfer ahead of next season. He was linked with major clubs including Milan and Inter during the spring.
According to BBC Sport, English champions Arsenal are now showing strong interest in the goalkeeper.
Kepa Arrizabalaga's future at Arsenal is uncertain, which is why the club are looking for a new deputy to first-choice goalkeeper David Raya.
Meslier fell down the pecking order at Leeds after a run of high-profile mistakes, and was pushed further back following the signing of Lucas Perri last summer.
He was registered as third-choice goalkeeper for the 2025-26 season behind Luca Perri and Karl Darlow, and did not feature in a single Premier League matchday squad across the campaign.
A move to a Premier League title-winning squad would offer Meslier the chance to compete for a place in the top flight again after a difficult year on the sidelines.
Arsenal's interest comes as the club continue to monitor their goalkeeping options for next season, with Kepa's situation adding to the uncertainty behind David Raya in the pecking order.
Meslier's availability on a free transfer, combined with his Premier League experience over several seasons at Leeds, is understood to make him an appealing option among the alternatives being considered at the Emirates Stadium.