The 32-year-old hasn’t featured for the Clarets in the Premier League since Boxing Day, after dropping down the pecking order since Tom Heaton’s return from injury.
Hart, who arrived at Turf Moor for £4 million last summer amid injuries to Heaton and Nick Pope, could cut ties with Burnley after just one season, according to the Daily Mail.
Sean Dyche’s side want to get the 75-time England international off their wage bill and several clubs in France are said to be interested in landing his signature.
The former Manchester City goalkeeper spent the 2016/17 season on loan at Torino in Serie A and is understood to be open to another move abroad.
Hart has struggled for consistency since Pep Guardiola’s arrival at Manchester City in 2016, enduring mixed loan spells in Turin and at West Ham before departing the Etihad for Burnley last summer.
He has made 19 Premier League appearances this season.
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