The Reds missed out on qualifying for the Champions League next season and they are looking to rebuild their on-field options this summer.
The Anfield outfit are on the verge of striking a deal for Argentine midfielder Alexis Mac Allister amid the departure of their veteran campaigner James Milner.
Jurgen Klopp’s side have been linked with several players, including Orkun Kokcu, Manu Kone and Khephren Thuram, and they have also been credited with an interest in Kessie.
However, it is suggested that Kessie is not on the wish list of Liverpool despite the claims that the Reds are willing to pay £30m to Barcelona for the Ivorian international.
Kessie, 26, joined eventual La Liga champions Barcelona from AC Milan last summer on a four-year contract.
Chiefly playing from the bench, the Ivorian international made 28 league appearances for the Catalan outfit this term and was booked four times, besides bagging one goal and one assist.
As Liverpool are claimed not to have Kessie on their transfer shortlist, it remains to be seen which of the other midfielders linked with the club they will move for.
