White has made a successful step-up to the Premier League with Brighton following his season long loan spell at Leeds last campaign.
The 23-year-old has been a virtual ever present in Graham Potter's Brighton team and has been a key figure in their impressive recent run.
Liverpool have suffered severe injuries at centre back with Virgil van Dijk, Joe Gomez, Joel Matip and Fabinho all sidelined. The Reds were heavily linked with a January swoop for the Albion academy graduate but instead completed a deal with Preston for Ben Davis.
White however remains a long term target for Klopp, who was said to be very impressed with White's display as Brighton secured a 1-0 win at Anfield earlier this season.
The defender, who can also play in midfield or wing back, is said to be happy at Brighton and is enjoying his football under Graham Potter. He recently signed a new long term deal with the Seagulls until 2024.
That hasn't however prevented the transfer speculation with Chelsea and Tottenham also said to be keen.
Potter remains calm about his defender's future and insists White is never one to let the speculation get to his head.
"He is a level-headed guy and he wants to play football at the very highest level," Potter said recently.
"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."
Greenshoots ahead of Brighton vs Crystal Palace
Graham Potter is beginning to see the fruits of his labour in his bid to establish Brighton in the Premier League.
Albion, in their fourth season back in the top flight, showed few signs of progress until January, winning only two of their first 18 league matches.
But they will bid to make it seven unbeaten in Monday’s home game against derby rivals Crystal Palace and Potter used a gardening analogy to explain their turnaround.
“My dad was a keen gardener and had his allotment,” Potter said. “He would always start off doing a lot of digging, a lot of heavy work, with not too much to show for it and a lot of back ache.
“Eventually, after a long period of time, he would start to see things coming through and he would have some vegetables. But it takes time. It’s like anything in life.
“We’ve had to try to change the playing style a little bit, we’ve introduced some younger players from the academy, taken some players that are adapting to life in the Premier League.
“To still get results in the Premier League is a huge challenge.”
Adam Webster injury
Brighton continue to have injury concerns ahead of their Premier League fixture against Crystal Palace at the Amex Stadium this Monday night.
Adam Webster (ankle) is unlikely to feature and Tariq Lamptey (hamstring) is definitely out.
Brighton head coach Graham Potter is however hoping Alireza Jahanbakhsh can return to the squad after missing the last nine games due to a hamstring injury and Danny Welbeck could be in contention having made substitute appearances against Burnley and Aston Villa.
“No he (Lamptey) wont be available on Monday that will be too soon for him," said Potter.
"But he is making good progress though, we are hoping that he will back with the group and the weekend and be back in training next week.
“Adam (Webster) is looking unlikely for the game we are still assessing the damage to his ligaments. So it looks quite likely he will miss the game.
"Danny (Welbeck) has been training well, so the only thing he has been lacking is game time. But we are building that up with training and he had a good session today.
"The same with Ali, he just needed a bit more time coming back from his injury, but he will be available for the squad on Monday night.”
Brighton provisional squad: Sanchez, White, Burn, Veltman, Alzate, Dunk, Bissouma, Gross, Mac Allister, Trossard, Maupay, Welbeck, Lallana, Jahanbakhsh, Connolly, Karbownik, Moder, Tau, Zeqiri, Propper, Walton.
Crystal Palace provisional squad: Guaita, Clyne, Kouyate, Dann, Van Aanholt, Ayew, Milivojevic, Riedewald, Eze, Benteke, Batshuayi, Butland, Ward, Townsend, Mateta, Cahill, Mitchell, Kelly.