The Reds signed the Belgian striker from the Ligue 1 side over the summer in a £10m deal, but agreed to send him back to northern France for the 2014/15 season to boost his development through regular playing time.
But with Daniel Sturridge set to be sidelined until January 2015, the Merseysiders are reportedly considering pushing to get the 19-year-old in early in a bid to keep their top four challenge on track.
The loss of their 25-year-old forward has come as a bitter blow, with the ex-Chelsea man having picked up his third injury of the campaign – he last played for the club in August.
In his absence the likes of Fabio Borini, Rickie Lambert and Mario Balotelli have all failed to register a Premier League goal, which has contributed to the club’s meagre tally of eight points from eight games.
Lille themselves have played down talk of Origi heading to Liverpool early, yet it’s understood that Rodgers is keen to get the teenager in ahead of schedule.
A potential deal may cost around £5m, with such a fee likely to tempt the club if the player himself makes it clear he wants the deal.