Karius had previously been largely restricted to appearances in the Champions League during the first half of the season, but he has now started the Reds' last two matches including Sunday's 4-3 Premier League win over Manchester City.
Liverpool boss Jurgen Klopp admitted that Karius was at fault for one of those goals, but was complimentary of his performance on the whole and is understood to be willing to give Karius an extended run in the starting lineup.
Mignolet is concerned that a lack of first-team football could affect his World Cup chances, though, and hinted that he could consider leaving the club.
"I have to stay calm. At the same time I have to think about my future. I am 30 years old and the World Cup is coming," he told The Times.
Mignolet has kept seven clean sheets in his 19 Premier League appearances so far this season.