However, the Mirror report that Hart will not sign for West Ham permanently after a disappointing season, but Wolves and Southampton are both in the market for a goalkeeper.
Hart has spent the last two seasons on loan at Torino and West Ham respectively, but has not done enough over the last two years to convince Gareth Southgate that he deserves a seat on the plane to Russia this summer.
The 31-year-old is due to return to Manchester City this summer, but will be on the hunt for a new club after failing to impress Pep Guardiola. He would struggle to break into the side ahead of Ederson, who joined the club for £35m from Benfica in 2017.
Southampton are one of the interested parties, with them reportedly keen to offload Fraser Forster, while they have received interest from other clubs for Alex McCarthy - who played a crucial role in securing their Premier League survival this summer.
The Saints could have an upper hand in any bid to sign Hart, with former Birmingham and England goalkeeping coach Dave Watson now working as Head of Goalkeeping at Southampton.
The Mirror report that Hart enjoyed working with Watson and even tried to get him a job at the Etihad Stadium.