The Scotsman is in charge until the end of the season after replacing Roy Hodgson in early January but after a string of good results, Carragher wants the Liverpool legend to stay on for longer than his initial stint.
Carragher does accept that this may not occur but put his case forward for the club to retain Dalglish well after this season ends.
"Things have improved now ad Kenny coming has got everyone onside," he said.
"That's not our decision. That's up to the club owners. For everyone, especially me and Stevie (Gerrard), he's a hero to us. The results are obviously going very well.
"If you're asking me, obviously I'd love him to be the manager."