"It's amazing really that he's been a player who's been able to dip under the radar as we think so much of him, not only his ability, but his mentality and his maturity," Southgate told British media.
"He's a very exciting player, but grounded, wants to improve all the time. For me he's going to be a top player. He has all the attributes of the top players I've worked with, but he's still only 20.
"Quite often we look across at each other in training and raise our eyebrows at some of the things he does. He's a very exciting player."
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Southgate said the faith shown in Rashford by United manager Jose Mourinho and former England boss Roy Hodgson was a sign that they considered him a big-game player.
"Jose (Mourinho) wouldn't mess around, but he picks him in all the big games and is on the field in nearly every game," Southgate said. "Roy saw the same things.
"We wanted to look after him last summer as we see him as a big part of our future. He'll score goals... his technique and his finishing ability are tremendous."
The striker, who has made 14 appearances for England, will look to add to his two goals when they play five-times world champions Brazil at Wembley.
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by Sudipto Ganguly)
