The 28-year-old joined the Citizens from MLS side Columbus Crew in 2019 as a backup to first-choice shot-stopper Ederson.
Steffen made just 21 first-team appearances under Pep Guardiola and failed to stake a claim for a regular starting spot between the sticks following a series of error-strewn performances.
Following the arrival of Stefan Ortega at the Etihad Stadium last summer, the USA international lost his place as No.2 goalie and was loaned out to Championship club Middlesbrough to gain regular first-team football.
Steffen made 44 Championship appearances for Boro, keeping 10 clean sheets, but Michael Carrick's side missed out on promotion after losing to Coventry City in the playoffs.
Steffen's future is now up in the air, with the goalkeeper recently admitting that he has 'no plans' to return to Man City.
Speaking to Philadelphia Inquirer last month, the American said: "I don't think I'll go back (to Man City). No, I want to be playing.
"Although I had a great time at City and I love those guys, and obviously an amazing club, I don't really have any plans to go back."
According to The Northern Echo, Man City are ready to sell Steffen this summer but will demand a fee of around £10m.
Steffen is under contract at the Etihad Stadium until June 2025 and is believed to be earning around £60,000 per week.
Middlesbrough are understood to be keen to sign Steffen on a permanent basis, but they could face stern competition from at least two teams in the Bundesliga.
Steffen spent the early stages of his career with Freiburg II in 2015-16 and he also represented Fortuna Dusseldorf on loan from Man City during the 2019-20 campaign.
Elsewhere, The Sun reports that the Citizens are looking to loan out young goalkeeper James Trafford to a Premier League club next season amid interest from newly-promoted duo Burnley and Sheffield United.
Trafford, an England Under-21 international, has been a standout performer for Bolton Wanderers in League One this season, keeping 22 clean sheets in 45 league appearances.