Hart has been on loan in Serie A since he lost his place as City number one after Pep Guardiola's appointment, a role subsequently filled by both new signing Claudio Bravo and Willy Caballero.
Torino head coach Sinisa Mihajlovic wants to keep the 29-year-old, who has played 29 league matches, but insists it would have to be a further loan agreement.
Mihajlovic, whose side are 10th in Serie A, called on City to decide quickly on whether they will loan out Hart again, amid reports the likes of Chelsea, Everton, Liverpool and West Ham are keen on a £15million transfer.
"I would like Hart to stay at Torino, but we know - the club and him too - that we can't buy him," Mihajlovic told reporters.
"At the most, we can take him on loan for another year, but it depends on what Manchester City want to do and what he wants too.
"We would like to know this soon because if we have Hart here next year then that is one thing, but if not we have to make other plans.
"Torino can only take him on loan for another year so it is up to City to decide, but we need a decision quickly so we can plan for the future."
Hart is under contract with City until 2019, but stressed last month he did not feel wanted at the club and would rather be somewhere he could play regular football.