Manchester City's keeper is eyeing a return to the Premier League.
Having spent the season on loan in Italy with Torino, the 30-year-old will be moved on permanently.
Pep Guardiola made his stance clear by signing Claudio Bravo and allowing Hart to leave.
Ahead of the summer, Manchester United and Chelsea are considering moves for the England international.
Joe Hart is on course to return from Italy this summer and join Liverpool
Hart is on his way to Anfield and will cost Liverpool £20million
However, according to The Sun, Hart is on his way to Anfield and will cost Liverpool £20million.
City were initially reluctant to sell to a direct rival, but that view has softened.
With two years remaining on Hart's current deal, City are ready to cash in.
Torino wanted to keep him for another season, as they cannot afford to buy him outright, although the Serie A side have apparently been told that won't happen.
Where could Joe Hart go next? Thu, March 23, 2017
Where could Joe Hart go next?
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Where could Joe Hart go next having fallen out of favour at Manchester City?
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Real Madrid's pursuit of David De Gea and Thibaut Courtois is said to have United and Chelsea eyeing Hart as a replacement.
But Liverpool have moved ahead in the race with Klopp still unconvinced by Simon Mignolet and Loris Karius.
Hart's experience and ability is seen as crucial to helping the Reds finally clinch a Premier League title.
Jurgen Klopp is aiming to build a team capable of challenging, and he is happy to spend £20m on Hart.