Hart is nearing the end of a season-long loan spell in Serie A with Torino, after City boss Pep Guardiola deemed him surplus to requirements at the Etihad Stadium last August.
Guardiola has indicated the England international will not form part of his long-term plans at the club next season, with a host of Premier League clubs now linked with a summer move for the 30-year-old.
Liverpool were among those sides, with their goalkeeping woes a constant talking point this season. Both Simon Mignolet and Loris Karius have endured spells out of the first-team this term but Klopp has no plans to bring in another shot-stopper with Danny Ward, who has enjoyed a fine season on loan at Huddersfield Town, also set to come into contention.
"He [Hart] is a fantastic goalkeeper, the goalkeeper of the England national team, so the highest quality," Klopp told a press conference broadcast through Facebook Live. "But we have high quality goalkeepers, that's how it is. He [Hart] is not for us at this moment and not in the future. That is not because of Joe but because we have two strong goalkeepers, Wardy at Huddersfield too playing a brilliant season so we will bring him back next year. There is competition. The situation around goalkeeper is good."
Karius, a £5m (€5.9m) summer signing from German club Mainz last summer, replaced Mignolet as Klopp's preferred choice in goal in September but was dropped three months later after high profile errors against Bournemouth and West Ham United. Mignolet would take over once again and has been Liverpool's no. 1 in league matches since.
Ward has enjoyed a terrific season as Huddersfield's no. 1 choice in the Championship this term, with the club currently sat in a play-off spot that could hand them promotion to the Premier League.