The 31-year-old has been at the club for 12 years, but following his omission from the England World Cup squad, now feels he needs to get more game time at a permanent club.
According to the Daily Mail, Hart has no intention of going out on loan again and Manchester City will have the opportunity to sell him for around £6m.
Hart has one year left on his contract at the Etihad, which is rumoured to be worth around £120,000-a-week.
He spent last season on loan at Premier League rivals West Ham, where he made 19 appearances for the Hammers in the league. However, a string of poor performances and mistakes meant that he spent the rest of the season as second choice behind Adrian.
His poor performances also meant that he wasn't selected for the World Cup this summer by Gareth Southgate, despite being the first-choice goalkeeper only two years ago at the 2016 European Championships.
Although he has not played in the league under City manager Pep Guardiola, Hart has plenty of experience, with 321 Premier League appearances to his name thus far. He has won four golden glove awards in that time, and two Premier League titles with the Manchester club.
The 31-year-old has also had a distinguished England career, earning 75 caps and travelling to two World Cups and two European Championships.