Klopp says he has not made a decision which will play against Porto in the Champions League last-16 clash tomorrow (February 14) but has hinted that Karius, who has started the last five Premier League matches for the Reds, could get the nod.
According to the report this could mean that Mignolet's "time is up" at Anfield and the 29-year-old could depart five years after joining from Sunderland.
While the Belgium international has never truly convinced during his time on Merseyside, the stopper still has 245 appearances in the top flight of English football to his name and could represent a decent addition to another club in the division.
The Magpies had been trying to improve in the position for some time, eventually signing Martin Dubravka on loan from Sparta Prague in January with the option of making it permanent for £3.5m at the end of the 2017/18 campaign - according to the Chronicle.
While Dubravka impressed on his debut in a 1-0 victory against Manchester United, a lot can still change between now and the end of the season in terms of who boss Rafa Benitez sees operating between the sticks on a long-term basis.
Meanwhile, West Ham have reinstated Adrian in goal with Manchester City loanee Joe Hart failing to impress and if Hart returns to the Etihad Stadium then competition will still be needed for the current Hammers number one.