The England forward has endured a frustrating start to the 2012-13 Premier League campaign, with a badly gashed leg requiring surgery following a collision with Hugo Rodallega.
However, the 70-year-old Scot feels that Rooney can now hit the ground running following a good period of training, expecting him to only get better as the season continues.
"Rooney is fit, he has trained really well," Sir Alex told reporters.
"I think Rooney will start scoring soon, once he gets a few games back. We know that, his track record tells you that each year he gets better with his finishing.
"I think Rooney will explode again soon. It is just the start of the season."The United boss credited the 26-year-old with working well during his recuperation period but warned that, because of Rooney's physique, he will have to maintain a high workload to remain fit and in the team.
"The period he was injured, I think that was key to it. He maintained his fitness which is important because he is a stocky lad," the Scot continued.
"He is very stocky, he is going to have to train well all the time, there is no doubt about that."
While Robin van Persie's early form - seven goals in eight games - may have taken the Old Trafford spotlight away from Rooney, Sir Alex insists that he wants the goals to be shared among his strikeforce.
"If you go back to the season before last, [Dimitar] Berbatov scored 20-21 goals, Chicharito scored 22 and Rooney scored 30-somethingm" he observed. "That was perfect, wasn't it?
"Two players there who took a load off of Rooney in that respect. I don't think it matters that much who gets the goals now.
"Van Persie has had a great start, seven goals. If him and Wayne and possibly one of the other strikers, Welbeck or Chicharito, get to around 20, we are in business.
"I think Rooney and Van Persie will [each] get over 20."