Arsenal and Juventus are also reportedly interested in the Bayern Munich midfielder.
The midfielder has been linked with an exit from the club all season having failed to establish himself since his move from Borussia Dortmund.
That could have changed next season as Carlo Ancelotti replaces Pep Guardiola at the helm of the German giants.
However, reports suggest that will not be the case, with the former Real Madrid manager allegedly telling Gotze in a phone call that his situation is not likely to improve.
That makes a move now extremely likely, and they are willing to accept as little as £15 million for his services according to Suddeutsche Zeitung.
A reunion with Jurgen Klopp at Anfield has long been mooted, and this news is likely to make them extremely confident of getting a deal over the line.
They are not the only Premier League side who are keen though, with Arsenal also named as a possible destination for him, while Serie A champions Juventus are also interested in his services.