The Yorkshire giants, who are preparing for life back in the Premier League, have seen White return to Brighton & Hove Albion following the end of his loan.
They want to buy White on a permanent basis, but Brighton are not playing ball and have knocked back proposals from Leeds for the centre-back.
If they fail to sign White then they will focus on Freiburg defender Koch, who is rated highly by Leeds director of football Victor Orta.
Leeds though are believed to have a third centre-back option in mind if needed.
It has not been confirmed who the club’s third option is, but they have been linked with a number of players, including River Plate’s Lucas Martinez Quarta.
Leeds are already without one of their centre-back options for a lengthy period, with Gaetano Berardi sidelined.
Skipper Liam Cooper is the only senior centre-back in the side, though Marcelo Bielsa trusted in 21-year-old Pascal Struijk on occasion last season and rates the former Ajax man.
