The two in-form rivals lock horns in the Merseyside derby at Anfield on Sunday looking to consolidate their excellent starts to the season.
Jurgen Klopp’s Reds remain unbeaten and are second in the Premier League, while Everton are beginning to find their feet under Marco Silva and have lost only one of their last six Premier League matches.
Shaqiri started on the bench as Liverpool lost 2-1 to Paris Saint-Germain in the Champions League on Wednesday night but could come back into the side to face Everton.
And Carragher – who was in Paris in midweek – has revealed he spoke to the Swiss star before the game to warn him of the importance of Sunday’s game.
“I pulled Shaqiri on the way out in the mixed zone in Paris,” he said.
“He came over and said: ‘Hello.’ I said to him: ‘It’s the derby on Sunday and you have to win, you have to win.’ He said: ‘I know.’”
Fellow summer signing Naby Keita might also be back in the team as manager Klopp is forced to make changes.
Jordan Henderson is suspended after being sent off against Watford last time out.
Keita has struggled to find consistency since his £53million move from RB Leipzig.
But Carragher has urged Klopp to give him a chance after watching the midfield three of Henderson, James Milner and Gerorginio Wijnaldum get overrun by PSG.
“I’d like to see Keita go in there,” Carragher added.
“It was built up that he was going to make a big difference to the midfield but we’ve only seen glimpses of it so far.
“You need to get him in the team, you paid a lot of money for this lad.
“Klopp knew him from Germany. I’d like to see him in there and see what he’s all about. Keita gives you more pace and energy with dynamic running.
“I think it will be a difficult game for Liverpool in terms of trying to break Everton down.
“It will be tight but Liverpool are so strong defensively.”