According to The Daily Star, Premier League United and Chelsea are both keen on signing the 21-year-old centre-back before the summer transfer window ends next month.
Despite being a former Chelsea player, retired midfielder Burley has said that the England international would be better off at United.
“I would go to Manchester United because it is a bigger club,” said the 43-year-old on the ESPN FC Show on BT Sport 1 on Wednesday morning. "It is not the most successful club at the moment, but it is the bigger club."
United are arguably the biggest club in the world along with Real Madrid and are aiming for the Premier League title this season.
It is a dream of many footballers to play for the Red Devils, and it would make perfect sense for Stones to move to Old Trafford.
Moreover, the youngster would have a better chance of breaking into the first team at United than he would at Chelsea.
Despite a less than impressive start to the 2015-16 Premier League campaign, Jose Mourinho’s side are defensively the best team in England (on paper).