The 30-year-old keeper is surplus to requirements at Man City. He's currently on loan at Torino, but is expected to leave the club at the end of the season.
Rumours of a possible move to Liverpool have been gathering pace in recent weeks, despite Simon Mignolet's return to form, but Klopp has quickly dismissed any possible move for Hart.
"He's a fantastic keeper, the highest quality, but it's not for us at the moment, nor in the future," said the German.
Source: DSG