The young England winger was undergoing a medical in Manchester on Friday ahead of a £15m (Dh87m) move from Championship club Crystal Palace.
The 20-year-old forward has agreed a five-and-a-half year deal but is being loaned back to Palace until the summer.
United will pay £10m up front, with the fee potentially rising to £15m based on Zaha's appearances and success.
"We like to sign young players with potential," Ferguson said Friday. "We can develop players well as we have proved many times, so hopefully the boy will enjoy it coming here.
"He's a winger, only a young lad, 20 years of age, so we will see."
Zaha, who joined Palace at the age of 12, is expected to win his second England cap against Brazil next month.
Both clubs have refused to comment on a proposed deal, but Ferguson has been heavily involved in the talks, having remained in England as his squad travelled to Qatar on Sunday for a short training camp.
Zaha, who came through the youth academy at Selhurst Park, has scored 15 goals in 124 appearances for the Eagles since his debut against Cardiff in March 2010.
Meanwhile, winger Ashley Young (knee) and Jonny Evans (hamstring) have returned to training but will not be considered for today's FA Cup fourth-round game at home with Fulham.
The tie marks the return of Dimitar Berbatov, 31, to Old Trafford after the Bulgarian striker, frustrated at his lack of first-team chances under Ferguson, called time on his four-year career at United in August.
Berbatov scored 49 goals in 108 Premier League appearances for United.
"He's their best player," Ferguson said. "I don't think Dimitar was a failure here. I think he did a great job here.
"The problem is, I had choices and at his age it's not easy to be part of those choices when he's not playing.
"He wanted first-team football and we gave him the opportunity to go to Fulham. At his age it was the right thing to do.
"He's done pretty well there. The problem here was the way we wanted to play, the selections we had. The hardest thing was when we had Tevez here also."
Berbatov's relaxed style on the pitch attracted criticism from some fans, but Ferguson said: "Some people like to see players run through brick walls all the time. Dimitar is not that type of player. But he's a very talented boy who had a decent goal-scoring record here."
Ferguson has been asked by the Football Association to explain his comments made about a match official during United's 1-1 draw at Tottenham last Sunday.
The Manchester United boss accused assistant referee Simon Beck of failing to give Wayne Rooney a "clear" penalty.
"I've put in my letter and we'll see what happens," said Ferguson, who labelled those who criticised the performance of keeper David De Gea at White Hart Lane as "idiots".