The Scotland youth international has been in top form recently and United are keeping tabs, though no deal is on the horizon.
United scouts are often present at Football League matches to run the rule over potential recruits but Burke has come under a particular amount of interest as they look to bring in new talent.
No move or bid is said to be imminent but Manchester United will continue to keep tabs on his performances after some impressive displays in recent weeks.
The wide man has recently been rewarded for good performances in the under-21s with regular first-team football at Forest. The Scotland youth international has scored two goals in his last four games and looks like an incredible talent for the future.
His pace and direct style have caught the eye and Forest will be hoping he continues to impress without heading out the exit door.
Recent recruits from the Football League at Manchester United have struggled, such as Nick Powell and Wilfried Zaha, so this would be a risk from United if they ever followed up their interest.
Forest fans need not worry for now and can be flattered that their star youngster is attracting such interest.