The England Under-21 defender shone in the Toulon tournament this summer.
The 20-year-old is one of the UK's best defensive prospects, having impressed since signing for Wolves two years ago.
The Mirror report that the Bundesliga outfit have scouted the defender already earlier this year, checking him out as the England Under-21 side won the Toulon tournament. They are said to be interested in a player who Wolves rate at £6 million.
Red Bull Leipzig
Hause moved to Molineux from Wycombe in 2014, having come up through the West Ham academy, with the youngster demonstrating his versatility during his 44 appearances at the club.
Kenny Jackett would be hugely reluctant to let a player of his potential depart so early in his career, but the former Millwall man will know that the best way to keep hold of prospects such as Hause is to make a real determined promotion attempt in the coming campaign.
QPR's Massimo Luongo in action with Wolves' Kortney Hause (L) and Richard Stearman
Wolves would have been disappointed to finish down in 14th position last season after an impressive 7th position finish in their return to the Championship the year before, what was Hause's first campaign at the club.
They will be aware that if Leipzig, backed by big money after storming up the German divisions following their Red Bull backed origin less than a decade ago, make a concerted move for the player, they may find it difficult to snub the several millions that may come their way.
Wolverhampton Wanderers' Kortney Hause against Blackburn Rovers