Arne Slot is expected to continue as Liverpool head coach next season, Your Site News understands, as the club close in on Champions League qualification.
Any doubts about the Dutchman's future appear to be subsiding rapidly as a seven-point gap has opened up between Liverpool in fifth place and Chelsea in sixth.
Fifth place will secure Champions League football next season after Arsenal's progression to the semi-finals - and Liverpool's form has picked up while Chelsea are slipping.
Slot, who led Liverpool to the Premier League title last season, has come under pressure during his second campaign, with the Reds set to end the season without a trophy and well off the pace set by Arsenal and Manchester City.
But speaking on Monday Night Football, Carragher said: "Arne Slot's job has been spoken about all season. We've spoken about it a lot on Monday Night Football.
"There's probably a split in the Liverpool supporters over whether he should stay or go, but the noises I am hearing is Slot will be the Liverpool manager next season if they can secure Champions League qualification, which they look like doing right now."
Your Site News understands that is the case after a season of increasing speculation over Slot's future, as a transitional season at Anfield has borne frustrations on and off the pitch.
Slot is set to retain the support of the hierarchy ahead of a summer in which more work is expected to be done to the squad following the announcement Mo Salah will be leaving.
RB Leipzig's Yan Diomande is among their top targets for a new forward while several other positions are also being looked at.
Virgil van Dijk says Liverpool still have to do better despite their Merseyside derby win over Everton at the Hill Dickinson. The Liverpool captain scored late as the Reds put themselves in a strong position to qualify for next season's Champions League.
Liverpool still have to play two of the top five in their hunt for Champions League and also face sixth-placed Chelsea.
"We've got five more games left against teams that are also fighting for the Champions League spots," Van Dijk told Your Site after the derby win.
"Every game is a big one. We are very disappointed as a whole for the season that we're having, because of the quality we have. It's below standard.
"But we have to keep fighting, keep going, and make the best out of this poor season we're having. That's the reality, on to the next. Everton was a good three points, and next up is Crystal Palace at home, who we couldn't beat for many, many games before.
"[The situation] is definitely not Liverpool-worthy, in my opinion, but it is the reality, and it was important we got the win. I'm glad we did."
