White has been excellent for Marcelo Bielsa's men this season, having joined on a season-long loan deal from Premier League club Brighton and Hove Albion.
Leeds, who are second in the Championship, would like to sign White on permanent basis, if they gain promotion to the Premier League.
But Brighton view White, 22, as a long-term replacement for their skipper Lewis Dunk, who continues to be linked with a move away from the Amex. Chelsea, Manchester City, Leicester and Arsenal are all admirers of Dunk's talents.
White has made 34 appearances for the Whites this season and has enjoyed his time at Elland Road. However, Albion's determination to keep their player - alongside added interest from Premier League giants Liverpool and Tottenham - means Leeds chances of securing White permanently are slim.
They have now turned their attention to SC Freiburg's German defender Robin Koch, who is rated at £15m. Koch has made 20 appearances in the Bundesliga this season and has been capped twice by Germany.
Elsewhere in the Premier:
Aston Villa's Jack Grealish, 24, will consider a summer move and Grealish sees Manchester United as his preferred destination, despite reported interest from Barcelona and Real Madrid.
Former Spurs manager Mauricio Pochettino remains in contention to become Manchester United manager next season and Uruguay striker Edinson Cavani, 32, linked with Manchester United and Chelsea in last month's transfer window, is open to a move to England when his contract at Paris St-Germain expires in the summer.
Manchester City's Belgium midfielder Kevin de Bruyne says he is comfrtable at the Etihad despite reports linking the 28-year-old with Real Madrid and Barcelona.
Former Arsenal midfielder Aaron Ramsey, 29, is already being linked with a move away from Juventus. He is just one year into a four-year contract.
Liverpool are keen to bolster their already fearsome attack. They are keen on RB Leipzig's Germany striker Timo Werner. But they are likely to sell 22-year-old Wales forward Harry Wilson, who is on loan at Bournemouth, this summer.