The report claims that both the clubs are in talks with the 24-year-old Frenchman who will be a free agent at the end of this month.
Rabiot was linked with a move to Tottenham and Barcelona as well, but both clubs weren’t keen to match his high wage demands.
Manchester United have made a formal offer to Rabiot, worth €10m a year with a €5m signing bonus, while Everton are also in talks with the Frenchman.
Liverpool already have a solid midfield set up, but Klopp could be tempted to sign a top class defensive midfielder.
Rabiot is a technically gifted midfielder and would definitely add quality and depth to the Liverpool side. He would be a fantastic addition to the side, no doubt, but probably he is not the type of player Klopp would be interested in signing this summer.