The midfielder has been the subject of intense transfer speculation in recent weeks amid rumours new Barcelona coach Ronald Koeman is eager to sign him.
Wijnaldum has less than a year left on his current deal at Liverpool and it did seem unlikely the Dutchman would pen a new deal.
Sky Sports claim, however, Wijnaldum has decided he wants to stay at Liverpool and snub interest from Barcelona.
Wijnaldum met with Klopp on Wednesday to discuss his future and the talks were ‘positive’, with the Liverpool head coach telling the 29-year-old he wants him to stay at Anfield.
Klopp poached Wijnaldum from Newcastle in 2016 and the player has emerged as one of the most influential figures at the club and is part of the first-choice midfield trio at Liverpool.
Koeman has worked closely with Wijnaldum in the international set-up and is desperate to overhaul his woefully underperforming and ageing Barcelona squad.
But Wijnaldum is hopeful Liverpool will offer him a new deal, even with the Reds’ reported interest in Bayern Munich star Thiago.
Liverpool are reluctant to meet Bayern’s asking price, but Thiago himself has already agreed personal terms with the Reds.
Klopp has played down criticism about Liverpool’s lack of transfer activity in the current window, with Kostas Tsimikas the only addition to the senior squad so far.
Liverpool welcome Championship winners Leeds United to Anfield on Saturday in their first Premier League game of the 2020/2021 season.
The Reds are gunning to win back-to-back league titles after ending their 30-year wait for domestic glory last season.