The 19-year-old moved north from Brighton for the season in July and has become an integral part of Marcelo Bielsa's defence.
So much so that two of the Premier League big boys are weighing up a move reports the Athletic.
Liverpool have a real interest in the central defender while United have scouted White as they continue their recruitment policy that places an emphasis on young homegrown talent.
The Seagulls loanee has made 16 appearances this season, but has never stepped foot into a top flight game.
His future beyond this season is up in the air with Brighton unwilling to include a permanent option in the deal that took White to Leeds in the summer.