The goalkeeper looks destined to leave Manchester City this summer.
Manchester City's Joe Hart looks dejected
Hart looks set to leave the Etihad this summer after failing to impress new manager Pep Guardiola.
The Spaniard has dropped him for their first two Premier League games, as well as the Champions League clash with Steaua Bucuresti.
With a move for Barcelona goalkeeper Claudio Bravo also on the cards according to BBC Sport, that leaves Joe Hart looking like he could be number three at the club in future.
Manchester City's Joe Hart during the warm up
That is not an ideal situation with an exit looking likely and Savage believes that Liverpool should be at the front of the queue.
“If I was Liverpool I would go for Joe Hart right now. He would go to Liverpool and be my number one,” he told BT Sport.
England's Joe Hart
It will certainly be interesting to see which clubs could make a move for Joe Hart before the end of the transfer window.
While Guardiola does not appear to rate the England goalkeeper, there is no denying he is a star and would represent a smart signing for a number of teams.
He would certainly represent an improvement on Liverpool’s options, although the signing of Loris Karius this summer makes a move unlikely.
England's Joe Hart celebrates after Jamie Vardy scored their first goal