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The 27-year-old is due to make his first return to Old Trafford next month, when the two clubs face each other in the Champions League and Sir Alex says the Portugal international has improved since leaving England.
“Maturity brings many things,” he told Inside United.
“When I went to see them play against [Manchester] City, some of his decision-making in terms of passing was brilliant. One-touch passing, good crosses.
“In the six years we had him, you just saw his game grow all the time, and he was a fantastic player.
“Now you see the complete player.
“His decision-making, his maturity, his experience, plus all the great skills he has got, they all make him the complete player.”
Manchester United travel to Spain for the first leg on February 13 before entertaining Madrid at Old Trafford on 5 March and Sir Alex is looking forward to the games.
“Obviously you hope that when you draw Real Madrid it’s in the final,” he said.
“It will be a big, big event – we’re the two most high-profile clubs in the world and I think they will be great games.”