The Belgium forward joined Liverpool from French side Lille in July but was immediately loaned back to the Ligue 1 outfit.
Origi, 19, has impressed so far this season for Rene Girard's men and has found the net four times in 12 appearances for the Stade Pierre Mauroy club.
But the teenager, who revealed he is in regular contact with Rodgers, is keen to make further strides before joining up with his new team-mates on a permanent basis.
"Brendan Rodgers keeps in touch when he can because he's a busy man," Origi said.
"Sometimes he sends me some messages and sometimes people from Liverpool come and visit me in Lille. It's good to know they are following my progress.
"Things are going well but there's still some room for improvement. I'm still working hard trying to prepare myself for a higher level. I'm feeling good and ready to continue this form."
Liverpool have made a stuttering start to the new campaign, suffering three Premier League defeats already, but they narrowly overcame West Brom 2-1 last week.
And Origi is confident Rodgers and his talented squad have what it takes to turn it around.
He added: "It's a new era at Liverpool and everything will go well. They have a fantastic team: [Mario] Balotelli is a great striker, they have Daniel Sturridge and they have Raheem Sterling - one of the best young talents in the world.
"It's only positive and I don't think we have to worry about Liverpool."
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