Origi is way down the pecking order at Anfield and hasn't played this season.
It's believed Wolves enquired about the 23-year-old Belgium international in the summer but were put off by a hefty asking price.
Liverpool are thought to want upwards of £20million for the 6ft 1in striker, who has scored 21 goals in 77 appearances for the Reds.
However Wolves hope that with Origi having only featured in one matchday squad this season, Liverpool could lower their demands or be open to a loan switch.
Origi's 'outstanding' attitude was recently praised by boss Jurgen Klopp but it's thought the Reds are still open to him leaving in January.
Origi, who joined Liverpool from Lille for £10m in 2014 and spent the 2014/15 and 2017/18 seasons on loan at Lille and Wolfsburg respectively, said recently: "At 23 I have big ambitions but for me it's just about focusing on the here and now and driving on as much as possible and hopefully let my feet talk on the pitch.
"I just hope for the best in everything and know that whenever I can shine my light it is a positive for everyone: for the club, for me, for the game that I am trying to impact... so I am really focusing on that."
Wolves have scored nine times in 10 games this season with their top scorer Raul Jimenez on two.
Addressing the lack of goals is likely to be their main priority in the transfer window.
The Express & Star understands that a meeting will take place in the coming weeks between the club's top brass to finalise their January targets.