The Dutchman is still at the relegated club, after joining last summer. The 25-year-old finished the season as the club’s top goalscorer, netting 11 Premier League goals, but was unable to keep the side in the English top flight.
The Magpies are keen to listen to offers of nearly double the £14.5million fee they paid for Wijnaldum last summer, but the Reds are hopeful they can negotiate a deal closer to the £20million mark instead.
Jurgen Klopp and his Liverpool team defeated Wigan 2-0 on Sunday, and head out to the United States of America for more preseason training, and club officials are eager to strike a deal before they board their flight on Thursday.
The Reds have already added to their attack this summer with Sadio Mane, but their German manager is keen to continue bolstering the Reds strike force, as he looks to get the club back into the UEFA Champions League.