The Belgium international forward signed for Liverpool in a reported £10 million deal in the close-season, but was allowed to remain with the Ligue 1 side for the 2014-15 campaign.
Brendan Rodgers' team have struggled in front of goal in the Premier League this season, with Daniel Sturridge plagued by injury and Mario Balotelli failing to score in the top flight since joining from Milan in August.
That has led to suggestions that Liverpool could explore the possibility of bringing Origi to Anfield early - and the 19-year-old would be willing to consider the possibility.
"It is not me who makes the decisions but if the club choose to let me go in January, I would join Liverpool," Origi told reporters.
"I said that I would stay for the whole season and I wish to remain honourable to that, of course.
"But if there was a decision by the clubs, I would not say that I would not like to go to Liverpool in January.
"I would love to move to Liverpool sooner rather than later.
"I can't wait to be playing in the Premier League because I can now see that it will suit me better. I think there are good things waiting for me with Liverpool."
