The Brighton defender had a superb loan spell at Elland Road last season, playing every minute of every game as Leeds won the Sky Bet Championship to be promoted to the Premier League.
Head coach Marcelo Bielsa wanted the 22-year-old to return to Yorkshire this season, with the player being the club's number one defensive target, but Brighton have steadfastly refused to discuss a deal and rejected several offers.
White has also been linked with several other top-flight sides including Chelsea, Liverpool and Manchester United.
"Unfortunately for the Leeds fans, Ben is just not going to be coming to Leeds," White's agent Alex Levack told Sky Sports.
"Brighton have categorically said there's no way that they are going to sell to Leeds. Unfortunately, that's the case.
"Ben's away up in Scotland with the Brighton team for pre-season, getting himself fit and around the team.
"But there's a lot of conversations happening. I would say watch this space over the next few days."