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Origi has played just seven minutes of Premier League football so far this season, falling down the pecking order following the arrivals of Takumi Minamino and Diogo Jota.
The 25-year-old striker was signed by Brendan Rodgers for Liverpool from Lille for £10m in 2015.
Rodgers was soon replaced by Jurgen Klopp and Origi scored 10 goals in his debut season at Anfield.
He hit 11 goals the next term but spent the 2017/18 on loan at Wolfsburg.
Returning to Merseyside, he turned down a £22m move to Wolves and played a major part in Liverpool's Champions League success that season, scoring twice in the memorable semi-final fightback against Barcelona and then the decisive second in the final against Tottenham.
However, he found the net just six times last term and has scored only once this season, in a Carabao Cup tie at League One Lincoln.
The frontman needs regular football in order to regain his place in the Belgium squad for the European Championships.
He was linked with a move to Aston Villa in the summer but decided to stay put and fight for his Anfield future.
"We have spoken with Liverpool and we have a nice course ahead of us," Origi said. "I just want to get better here.
"It is a project for me, and I want to follow it."
Wolves have a long list of strikers they're assessing for January. Divock Origi, a player they've courted before, is one of them. And Liverpool may be willing to let him leave. With @JamesPearceLFC #WWFChttps://t.co/jBn1ajItfx- Tim Spiers (@TimSpiers) December 17, 2020
However, the subsequent lack of football means Origi could now be open to an Anfield exit, with Wolves potentially his next destination according to The Athletic.
The Molineux side are in need of a centre-forward with Mexico international Raul Jimenez recovering after surgery on a fractured skull.
Wolves have scored just 13 times in 13 games this term and young Fabio Silva is the first-team squad's only recognised striker.
Origi is valued at £20m, but a loan deal is also an option.
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