The 19-year-old came off the bench to score in the 1-0 victory over a United States Under-23 side at Preston and looked the sharpest of Southgate's players even though it was his debut at that level.
However, Wilson's place at Old Trafford is under threat from the arrival of the signing of record-breaking £36million French teenager Anthony Martial and there are suggestions he may be farmed out on loan.
He has yet to make an appearance this season and has played just 17 minutes of first-team football since February.
Southgate has no intention of telling Louis van Gaal what to do with Wilson but is confident he will come good under their guidance.
"That is for him and his boss to decide," was the response when asked whether Wilson should go out on loan.
"I believe United will handle his development in the best way
They are one of the best clubs in the world
Look at their history for developing young players
"There is still some physical development to come
As he plays more matches he will get hardened.
"It is very early stages of us working with him
We've seen him play for United.
"He hasn't got enormous game time under his belt
We might have to be patient and wait for him.
"We know he is a goalscorer, and he has got some great potential."
Southgate also did not want to get drawn into the saga involving West Brom and Saido Berahino, a player he knows well from his work with the under-21s.
Berahino appeared to suggest via social media he would not play for the club again after the Baggies denied him a deadline-day move to Tottenham.
"You speak as you find people and Saido was super for us," he added.
"We enjoyed his personality and his football for us
He has a lot of potential.
"I'm sure he will sort things out with West Brom, I'm sure he will play for Tony and get on with him."
Source : PA
Source: PA