The England goalkeeper has said he is "surplus to requirements" at City.
Hart has spent the season on loan with Torino.
Several Premier League clubs are keeping a close eye on Hart ahead of a possible summer transfer, while Torino have confirmed they want to keep the 29-year-old.
"At the most we could take him on loan for another year but that depends on both Manchester City and him".
"We want to know soon, because if we have Hart next year..."
He wrote that his sources had told him that Hart is "not, hasn't been at any point and won't be in future [a] Liverpool transfer target".
Hart was never part of Manchester City boss Pep Guardiola's plans when he arrived a year ago and has spent the season on loan at Torino.
Earlier this week, City boss Guardiola rebuffed a question about whether Hart could have his loan spell in Turin extended.
Hart is now on loan from Manchester City, who let Hart leave for Serie A after they signed Claudio Bravo from Barcelona for £17m.
Torino manager Sinisa Mihajlovic admitted on Saturday that the Serie A club can not afford City's asking price, per Jamie Gordon of The Sun.
"Every weekend I will decide who is in goal, " added the Catalan manager.
Claudio Bravo has struggled since signing for £15.4 million from Barcelona last summer.
Turkey's premier calls on opposition to respect referendum
Cigarette Packs Could Cost At Least $13 Apiece Under New Legislation
Pence says US stands by ally Japan on North Korea problem
Loud sex sounds interrupt pro tennis match in Florida
Blue Jackets, Wild in danger of being swept out of playoffs
United States crude oil stocks drop
United Airlines not to fire employees who dragged passenger
Bill O'Reilly's statement following his firing from Fox News
Lookout notice against him, Dinakaran calls meeting of party MLAs
Why Patrick Beverley's Game 1 performance was best of his career
Trump to meet Palestinian President Mahmoud Abbas on May 3
Pence: US won't rest until N. Korea gives up nuclear weapons
United passenger: 'I'd rather go to jail' than leave flight willingly
Bernie Sanders kicks off cross-country tour in Maine
Half Girlfriend movie Phir Bhi Tumko Chaahunga song is out; Watch now
Saturn's Moon Enceladus Could Have Conditions for Life
Star QB Tom Brady to miss NFL champs' visit to White House