White has been excellent for Brighton this season and made an encouraging start to his first full campaign in the Premier League.
White was on loan at Leeds last term and was one of their stand-out players during their title-winning campaign in the Championship.
The Whites were determined to sign him on a permanent basis and Marcelo Bielsa's men made three bids north of £20m last summer but Albion held firm.
The 23-year-old has made the step-up to the Premier League with Brighton look relatively comfortable and has featured in midfield and defence for Graham Potter's men.
His displays continue to alert the giants of the game and Jurgen Klopp's Premier League champions are said to be in pole-position in the race to sign the Brighton academy graduate.
White signed fresh terms with the Seagulls at the beginning of the season and is contracted until June 2024.
It would take serious money to prise this talent away and White has been valued at anything between £25m and £50m by various outlets in the past 12 months.
Sky Bet currently have Liverpool at 7/2 to sign White this January, with Leeds and Manchester United at 25/1. Man City are also said to be in the running at 20/1 and Tottenham (16/1) also feature in the betting.
However, Albion head coach Potter is not worried by the speculation and insists White will not have his head turned.
"He is a level-headed guy and he wants to play football at the very highest level," Potter replied.
"He gets down with his work. He was totally professional in the summer, despite the noise outside which you cannot control.
"He is a smart guy. We will try to help him enjoy his football as that is the most important thing."