The £16.5million summer arrival from Blackburn has impressed at the start of his United career and Pallister thinks the 19-year-old has what it takes to rise to the top.
He told the Daily Mail: "It's easy to get carried away with his start at Manchester United. But you have to look at the maturity he's got and the type of character he is.
"He dictates to other people on the pitch, which is very rare for a young lad, and it shows he has a lot of confidence and belief in himself. He has been right out the top drawer.
"You never know the pitfalls ahead, but on talent alone he has a big England future.
"He has been absolutely outstanding. I didn't expect him to play too many games so early in his career there, but injuries to Rio [Ferdinand] and Nemanja [Vidic] have seen him come in and look an outstanding prospect.
"He plays with great maturity and doesn't appear to have any kind of weakness in his game.
"He looks a real big star of the future. For a player to come in at that age and be as settled as he is says a lot about the kid's temperament."