According to Sky Sports, Ramos is a target of the Old Trafford club, who are unsurprisingly in the market for defenders after last season's questionable performances.
The talk could be a matter of Ramos flirting with the idea of getting a bigger and better contract from Real Madrid but United should not allow David de Gea leave in the other direction cheaply.
If the Premier League giants play hardball, they could possibly end up with another great player in return to soften the blow. Goalkeepers like de Gea don't come around too often.
However, the reaction among Manchester United supporters has been mixed. Forgetting about all Ramos has won through his career at club and international level, a lack of discipline has worried many.
Carragher, primarily a centre-back throughout his career, does not agree with those critical of Ramos and believes the Spain international would be a great acquisition for Louis van Gaal.
“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?"
Is Sergio Ramos playing his cards right for a new Real Madrid contract?
This could be one of the reasons Manchester United fans are proving reluctant to get too excited over the possibility of signing Sergio Ramos. Already this summer Dani Alves' agent flirted with the idea of leaving Barcelona before signing a new bumper contract with the club.
It is a game many agents and footballers play as it works more times than not. Whether or not it is the case with Ramos, United should not allow David de Gea to leave unless they get a player in return. And not just any old player. Someone that would make a difference.