According to the BBC, the 26-year-old Frenchman became a free agent this summer after his contract with the Championship club expired, bringing an end to his five-year stay at Elland Road.
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Meslier played a key role in Leeds' promotion challenge during the 2024-25 campaign but lost his place to Karl Darlow for the closing stages of the season.
He later slipped to third choice behind Darlow and Lucas Perri before being released.
Arsenal are reportedly assessing the goalkeeper market amid uncertainty over Kepa Arrizabalaga's long-term future as David Raya's deputy.
Meslier's Premier League experience, availability on a free transfer and familiarity with English football make him an attractive option for the Gunners.