The 21-year-old’s debut season in the Red Devils' first team saw him notch nine goals in the Premier League and earn himself a call-up to represent England at Euro 2012, where he scored the winner against Sweden in the group stage.
And Sir Alex has admitted that he has been impressed with the striker’s development and believes that he is ready continue improving next season and become an integral part of the Old Trafford setup.
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He told Press Association Sport: "We are negotiating with Danny's brothers. They represent him. It's difficult to say where we are with that at this moment in time.
"If you look at the games he played for England at the Euros, he's never played three games in seven days before - well, certainly not for us. So he did really well in that respect. That's where maturity and development comes in.
"We've fostered him. He's always had growth spurts and things like that, so we fostered him right that period when he was developing. I don't think he's got his full body yet. I think there's a lot of growth in him yet. I don't think he'll get taller, he's six-foot-three now.
"He's very powerful and, once that growth thing stops, I think you'll find he can play three games in seven games. There won't be a problem with that. He's got good movement, courage and confidence with the ball.
“Obviously, he will have to improve his goalscoring. I think he got nine goals last season but if you are going to be a top striker you have to get 20 goals or above. That will happen to him, I think he will do that."
However, Welbeck’s United team-mate, Wayne Rooney, did not impress as much in Poland and Ukraine, and Sir Alex is of the opinion that the striker’s two-game suspension meant that he was less fit than the rest of the squad.
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"Where Wayne has improved is his consistency in scoring goals,” the Scot added. “He got 32 goals last season and that has made a difference to his game. It's difficult to say whether he is at a peak or not but his goalscoring has certainly given us more of a reward.
"We know him better than anybody. If Wayne misses couple of games, it takes him three or four to come back. He needs a lot of football. He’s a big lad. He is stocky and he needs a lot of games.
"I always thought it was a bit of a difficult one really. He’d not played since his last game on 13 May until he played the third game of the Euros more than a month later.
“I don’t know what his stats were but he certainly didn’t look as sharp as normal. When he played one big game in four days and then had to play another one, that is very hard."