Enrique, 25, joined The Reds from Newcastle United for around Â£8m in August and the Spanish left-back has effortlessly slotted into Kenny Dalglish’s side.
And Carragher feels his Liverpool team-mate is unfortunate not to be involved in Vicente del Bosque’s Spain squad with Euro 2012 on the horizon.
“He’s settled in really well, you can see that in his performances,” said Carragher. “He mixes in well with the lads, has a laugh and a joke.
“I’m very surprised he hasn’t had a Spain call-up. It makes you realise how strong Spain must be, because I can’t think of a left-back who’s performed better than him at this stage of the season.
“You wonder what they’ve got at left-back, but if he keeps performing the way he is he’s got a chance of getting in for the Euros in the summer.
“Spain are a great team but their weak position is left-back. That is a position that’s up for grabs, so with the way he’s playing for a top club, he deserves a chance.”
Meanwhile, Carragher revealed he hopes to recover from an injury in time for Liverpool’s trip to Stamford Bridge to face Chelsea on 20 November.
“I’m back on Sunday and then hopefully I’ll get back in with the lads, what’s left of them, on Monday,” said Carragher.
“It’s the best time to be injured because you don’t miss too many games.
“It’s down to the manager and the coaching staff, but once I’m back with the lads I’m back, for the squad, the team or the bench – whatever it may be.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news