During the summer, Liverpool boss Jurgen Klopp allowed Origi to sign a season-long loan deal with the Bundesliga side, with first-team opportunities expected to be limited at Anfield.
The form of the Belgian attacker has led to Wolfsburg opening discussions with Liverpool over pushing through a transfer of the 22-year-old.
Origi has contributed four goals and one assist in 15 league appearances since leaving Merseyside, and he is yet to miss a match for his current club.
Wolfsburg sporting director Olaf Rebbe told Kicker: "The people at Liverpool are merchants, no Samaritans. We will still try to exhaust our possibilities, alongside the player who feels well here."
Origi has 18 months remaining on his contract with Liverpool.