Ramos is on United’s radar and newspaper reports claim United are demanding Real Madrid’s long-serving centre-back as part of any deal for goalkeeper David De Gea.
But the reaction among United supporters to the Ramos interest has been mixed, with the 29-year-old Spain international’s poor disciplinary record a key concern.
Former Liverpool centre-back Carragher insists Ramos would be a great acquisition for United boss Louis van Gaal, though, and is bemused at the opposition to a player who has won three La Liga titles, a Champions League trophy, one World Cup and two European Championship medals.
“I get a bit wound up by the criticism Ramos gets,” Carragher told talkSPORT.
“This is a fella who has won everything, he plays for one of the best clubs in the world and one of the best international sides we’ve ever seen.
“He is rash at times, he has moments of madness and does get overly emotional in games, that’s always been a problem for him, but let’s not forget that it’s a problem for Wayne Rooney as well.
“I’m not bothered about whether United sign him or not, or whether he’d be a good signing or not, but if he is not rated as one of the world’s best players, who is?
“If his trophy record doesn’t give him a bit of credit, what chance have I, or any of the centre-backs in the Premier League?
“I think it’s disrespectful – he’s won nearly 130 caps for Spain! He’s not playing for Mickey Mouse teams.
“I’ve heard callers say he hasn’t reacted well under pressure and he makes mistakes – what defender doesn’t make mistakes?
“If a team like Real Madrid could find a better defender, they would, but they don’t. Ramos plays every week, they win everything and people still chip away at him and criticise him.
“Top-class centre-backs are a dying breed now, there’s very few now compared to years ago. If United don’t get Ramos, or don’t want to sign him, who else would they get?”
Sky Sports’ Spanish Football Expert & Columnist Guillem Balague is not sure Ramos will be on his way to Old Trafford, however, due to a €200m (£143m) buy-out clause in his contract at Real.