The 24-year-old joined Salzburg in 2019 for around £10.6m, becoming the most expensive player in the Austrian Bundesliga.
The Austria international began his career as a centre-back, but he has started regularly as a left-back this term, scoring twice and providing six assists in 21 appearances across all competitions.
The centre-back has features 125 times for Salzburg and has won three Bundesliga titles and three Austrian Cups.
According to Fabrizio Romano, Leeds United have reached an agreement to acquire Wober from RB Salzburg for a fee of over €12m (£10.6m).
Romano adds that both sides are now preparing the paperwork before the deal can be finalised this month.
The Yorkshire giants have also been linked Club Brugge winger Noa Lang and Southampton striker Che Adams in order to strengthen their squad for next season.
Leeds are currently 14th in the Premier League standings, barely above the relegation zone with just two points.