The 23-year-old centre-back is poised to become Dean Smith’s second signing of the January transfer window following talks between the Midlands rivals.
Hause, who joined Wolves from Wycombe in January 2014, has been limited to just six appearances during the past 18 months, the last of those coming in September.
But he remains a player with considerable potential, while his ability to also play at left-back is also thought to appeal to Smith.
The head coach has put strengthening Villa’s defence top of his January agenda and has already secured the signing of Croatia international Lovre Kalinic, in addition to recalling Tommy Elphick from Hull.
Smith remained non-committal when quizzed about Hause following Villa’s 2-2 draw with QPR on New Year’s Day.
He said: “I could be close to signing anybody. We have a number of players we’re looking at.”