The Brazil international has struggled to make an impression at the La Liga champions since his £142m move to the Camp Nou from Liverpool FC in January 2018.
Coutinho was criticised in Spain for his performance in FC Barcelona’s 4-0 loss to Liverpool FC in the second leg of their Champions League semi-final earlier this month.
The 26-year-old has been linked with a potential switch to Chelsea FC, who are preparing for Eden Hazard’s expected move to Real Madrid this summer.
Former Liverpool FC defender Carragher would like to see Jurgen Klopp explore the possibility of bringing Coutinho back to the Anfield outfit ahead of the new Premier League season.
“I wouldn’t say I would be actively going to get him, but if there was a possibility of bringing Coutinho back for decent money, and Barca wanted to cut their losses a little bit because it hasn’t worked out, then I’d do that,” Carragher told the Liverpool Echo.
“Would he be welcomed back? I’m not sure. But he should be. I don’t see any reason why he shouldn’t be.
“I know he got a little bit of stick when he came back (with Barcelona for the Champions League semi-final earlier this month) because he wanted to move.
“But Alonso wanted to move to Real Madrid, Suarez wanted to move to Barcelona, and we still loved them when they went.
“Sometimes we pick and choose who we love when they leave. Nobody forced any player to go to Real Madrid or Barcelona, Mascherano is another one.
“Suarez only got stick when he came back because of his antics in the first game (against Liverpool), if he hadn’t done that then he’d be adored when he came back. What’s the difference between him and Coutinho?
“We lack that player in the squad. We have it in Lallana and Shaqiri, but this is a different level of player.
“It’s the one thing Man City have on us, they have Bernardo Silva, David Silva, Kevin De Bruyne. We don’t have that type of player.
“We have great midfield players who are all very similar. We could add something a little bit different.
“But that would only really be if it was a good price for us.”
Coutinho moved to Liverpool FC in an £8.5m deal from Serie A giants Inter Milan in the 2013 January transfer window.
The Brazilian playmaker scored 54 times in 201 games in all competitions over five seasons at the Merseyside club.
Coutinho didn’t win any silverware during his stint at the 18-time English champions.
His sale raised funds for Liverpool FC to sign Netherlands international Virgil van Dijk from Southampton in a £75m deal.
The Dutch centre-half was voted the PFA player of the season this term.
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