The central defender is an up-and-coming star in a Canaries side pushing hard for promotion to the Premier League.
Godfrey’s form has earned him a call-up to England Under-20s and put him firmly on the radar of United and other top-flight outfits.
The centre-back has not missed a single game since breaking into the Norwich team at the turn of the year, scoring three goals in the process.
And according to The Scottish Sun, United are considering making a move for the talented 21-year-old as they look to add strength in depth to their backline options.
United scouts watched Godfrey in action against Rotherham last weekend – when his goal salvaged three points for the Canaries.
The Red Devils have been looking for young centre-back who is comfortable on the ball for a while and it seems Godfrey fits the bill.
Godfrey started his career with York City’s youth system, before moving to Middlesbrough in the summer of 2011.
After being released by the club, he had trials with Leeds United and Sheffield Wednesday, before returning to York.
Links between Godfrey and Man Utd emerged amid news of:
In January 2016, Godfrey signed for Norwich on a three-and-a-half-year deal and made his debut aged 17.
Interim United boss Ole Gunnar Solskjaer seems likely to be given the full-time role in the not-too-distant future.
And he has already gone on record to say he in a fan of bringing young players through the ranks.
Victor Lindelof has missed just one game since the Norwegian took over in December.
The Red Devils caretaker clearly considering Lindelof his first-choice defender.
Eric Bailly, however, seems to have run out of chances and his United career could well come to an end this summer.
While Kalidou Koulibaly has been heavily linked with a move to Old Trafford, Napoli have attempted to put a deal on ice by placing an enormous price-tag on him.
United will look to bounce back from consecutive defeats when they return to Premier League action after the international break.