Reports this week suggested that Rodgers is willing to pay an additional fee to bring highly rated teenager Origi - who signed for Liverpool in the close-season but was left with Lille on loan for the 2014-15 campaign - to Anfield in the next transfer window.
Liverpool's need for extra firepower this season has been well documented and, after Daniel Sturridge's latest injury setback, Rodgers looks set to have to rely on Mario Balotelli, Rickie Lambert and Fabio Borini - who have failed to score a single Premier League goal between them this term - until the new year.
However, despite his parent club's desperate need for goals, it appears that Belgium international Origi will remain in France until the end of the season.
"[Origi is] a young player we signed last summer. [The deal] was on the agreement that he had to stay at Lille," Rodgers told a media conference on Friday.
"That was one of the main reasons we were able to sign him.
"As far as I'm concerned, that's still the case."
Sturridge, who scored 21 Premier League goals last season, has not featured for Liverpool since August due to thigh and calf problems.
The England forward was expected to return at Crystal Palace on Sunday, but broke down with a recurrence of his thigh injury in training this week and is now set to be out for up to another six weeks.
Sturridge himself has gone on record as saying he feels his persistent muscular problems may be hereditary, but Rodgers was quick to dismiss any suggestion that the former Chelsea man could do more to keep himself fit.
"Daniel has just been extremely unfortunate," the Northern Irishman added.
"He's a player who doesn't want to be out for this period of time with the quality he has.
"I spoke to Daniel at length and he's as down as I've seen anyone. We need to go away and find answers so he can perform consistently."
Rodgers also confirmed that Balotelli is facing a late fitness test to determine if he is fit to play at Selhurst Park after picking up a minor hamstring problem while on international duty with Italy, although Jordan Henderson is available after recovering from a similar complaint sustained while away with England.
