A Spor says Wijnaldum has been given the green light to join his former boss Philip Cocu at Fenerbahce.
The 27-year-old played 33 Premier League matches last season, scoring one goal and supplying two assists.
But he is concerned that Jurgen Klopp's summer arrivals will see him barely feature next season.
Fabinho and Naby Keita both occupy midfield roles and Wijnaldum fears that he could find himself further down the pecking order.
The Dutchman arrived from Newcastle in a £23m deal just under two years ago.