The German goalkeeper, who has recently recovered from a broken hand, replaced the Belgian in Jurgen Klopp's line-up in the 5-1 win over Hull City on Saturday, having debuted in the EFL Cup against Derby County midweek.
The game against the Tigers was Karius' first start in Premier League, displacing Mignolet, but he has made it clear that there is no ill-will between the pair.
"Obviously Mignolet and I train really well because we know we have a strong opponent so I think it is positive for us and the club," he said.
"We know we have to be at our best to play otherwise there will be another strong keeper waiting.
"It is really healthy competition and we don't have anything against each other and we try to help each other in training and get on okay so there is no issue between us.
"The one who doesn't play is going to be frustrated but the manager has to pick 11 players."