Hart is considered to be surplus to requirements at the Etihad Stadium after being given permission to spend last season out on loan at Torino.
However, according to The Sun, boss Pep Guardiola has taken a different stance this summer and he is looking to sell the England stopper to the highest bidder.
It has been claimed that both Newcastle United and West Ham United hold an interest in the 30-year-old, who is looking for first-team football in order to boost his chances of remaining first choice for the Three Lions ahead of next year's World Cup.
The suggestion is that City believe that both clubs have the financial clout to meet their £18m valuation and City will not benefit from allowing their long-serving player to spend another season playing for another team.
Since moving to the club in 2006, Hart has made 348 appearances in all competitions, while he featured on 37 occasions during his time at Torino.