McCarthy believes Jones will become one of the top players in Europe.
He said: “I thought United would sign Phil Jones in the summer.
“I remember talking to Sir Alex about players and I said he was one of the top players, and I sensed he already knew that, but I was offering my opinion.
“It was no surprise at all that they signed him. I think he’s one of the best around, whether he plays at centre-half, full-back or wherever.”
McCarthy added: “This is a kid of 19 or 20, and the only other bloke who played like that was Paul McGrath.
“He played for Ireland in midfield – and thank God he did because I wouldn’t have played otherwise (at centre-back).
“I kept saying to (manager) Jack Charlton ‘McGrath’s a great midfielder!’
“Paul got into the best World XI in 1990 as a centre-back playing midfield. That’s remarkable.
“But I also think Phil Jones has got everything – he’s just a fabulous player. He’s got a great attitude too.”
McCarthy added: “He played here against us for Blackburn and he was just dominant.
“He breaks out from the back with the ball and he’s quick, he’s good in the air, he seems to have two good feet. He’s just got everything as a footballer.
“I would say he is nailed on for England’s Euro 2012 squad.
“I really think he’ll be one of the best players in Europe for a long time because he’s fantastic.”