Hart has been in fine form for Torino since leaving Manchester City on loan back in the summer.
The England international departed the Etihad having fallen out of favour under Pep Guardiola.
Despite his replacement Claudio Bravo struggling to adjust to life in the Premier League, Hart is expected to leave City permanently at the end of the season.
But Torino chief Urbano Cairo has hinted a prolonged stay in Serie A could be on the cards.
Joe Hart could yet extend his stay at Torino
Joe Hart was unfancied by Pep Guardiola at Manchester City
Top six Premier League club's goalkeeper save percentages
Thu, January 19, 2017
Which top six goalkeeper has the highest save percentage so far this season?
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Claudio Bravo (Manchester City) – 28 per cent
"Nothing has been decided," Cairo said in a press conference when asked about Hart's future.
"When his loan expires we will have to talk to City.
"(New signing) Milinkovic-Savic is 19. If [head coach] Sinisa Mihajlovic sees him as the Serbian Donnarumma, he may opt to focus on him as a starter.
"Nothing is decided with Joe Hart, though.
"We will discuss it with him and the club and see what the conditions are.
Chelsea ace Thibaut Courtois could leave in the summer
"Nothing is defined from this point of view."
West Ham want Hart to replace Adrian.
The Hammers goalkeeper has toiled this season and Slaven Bilic wants the City goalkeeper to be his long-term replacement.
Chelsea are also keen amid uncertainty over Thibaut Courtois' future.
Courtois has been linked with Real Madrid, who want to sign him as an alternative to Manchester United goalkeeper David De Gea.