Widespread reports have indicated that manager Jose Mourinho could move for a defender in the summer window.
Varane has been linked to the Premier League club for some time, but Burley thinks that the Red Devils' style of play would put him off completing a transfer.
"Forget it. Why would you leave Real Madrid to go to Man United? Have you seen them play?" Burley told ESPN. "Honestly, why would you go to that team at the moment from Real Madrid? Not happening."
United faced criticism for their defensive display in last weekend's 1-0 defeat to Newcastle United.