The Whites’ interest in the centre-back emerged during the international transfer window, but Hamburg were not willing to let the 21-year-old depart.
Leeds director of football Victor Orta is a big fan of Ambrosius and the club could go in for him in the January transfer window, which is just 12 weeks away.
Hamburg want to see Ambrosius put pen to paper to a new contract, which would leave the German giants free to reject offers for him.
If he does not pen a fresh deal, he will be able to sign a pre-contractual agreement with a non-German club in January.
Ambrosius has turned out twice for Hamburg in the new 2.Bundesliga season, helping his side to wins over Fortuna Dusseldorf and Paderborn.
Speculation over his future is likely to ramp up as the January window approaches if he has not committed his future to Hamburg.
Hamburg are next in action after the international break when they take on Greuther Furth away from home.