The Reds have been lauded under Jurgen Klopp this season, although criticism has surrounded both Anfield stoppers, Simon Mignolet and Loris Karius.
Hart was booted out of City by Pep Guardiola, who chose to spend £15m on 33-year-old Claudio Bravo.
The England stopper took solace with a year-long loan deal at Torino, and the Turin outfit sit a handy eighth in this season’s Serie A.
Hart has made no secret that his stay in Italy will be a single year at the most, and few would argue he would be a great benefit to Liverpool’s title hopes.
But while the Merseysiders lead the betting, Chelsea can’t be ruled out, thanks to goings on in Madrid.
After Real’s transfer embargo was cut short, Los Blancos are free to make signings next summer, and one of their targets is reportedly Chelsea keeper Thibaut Courtois.
The Belgian is no stranger to the Spanish capital, after spending three seasons on loan at Ateltico Madrid.
Real have been linked with both Courtois and Manchester United’s David de Gea in recent years, and it doesn’t look good for current keepers Keylor Navas and Kiko Casilla at the Bernabeu.
So Chelsea may feel they have to move sooner than they would ideally like to sign Hart, for fear of missing out on him in the summer while also potentially losing Courtois.
All Odds and Markets are correct as of the date of publishing