The 19-year-old has been discussing fresh terms with Liverpool for several months, and the club are now believed to be close to reaching an agreement.
Liverpool rejected a £30 million offer from Nottingham Forest late in the summer transfer window and have since given Nyoni an increasingly important role in the squad.
The midfielder has made seven Premier League appearances this season, already exceeding his total from the whole of the previous campaign. He also made his full league debut in Sunday's 1-0 defeat against Arsenal, impressing before being replaced by Dominik Szoboszlai in the second half.
Liverpool's decision not to recruit a replacement following Curtis Jones' move to Inter Milan reflected their confidence in Nyoni's ability to step up.
Head coach Andoni Iraola has been encouraged by the teenager's development and wants him to continue building experience at senior level.
"I think he has to continue in that same place he's been since the start of the pre-season, being ready for every game," Iraola said ahead of Wednesday's Champions League meeting with Fenerbahce.
"He has played in all the games or at least all the games lately, so we trust him, he's doing very well. I think we have to encourage him to continue, you know? Continue improving, continue learning, continue adding experience. But he is in a very good place."
Iraola also highlighted the physical demands of playing regularly at the highest level, particularly for a young midfielder still adapting to the senior schedule.
"Is he ready for the schedule? I think that young players are already ready, you know? It's just that maybe one day you have to help us for 20 minutes or start and play 65, or maybe a full game.
"He is also adding endurance because sometimes when you are young, you feel OK, you are not going to get tired but you need to add this to your body."
Nyoni signed his previous contract in June 2025, but Liverpool are keen to recognise the progress he has made over the past 18 months with improved terms.
The club's willingness to reject a substantial offer from Forest and offer him a more prominent role underlines the confidence they have in his long-term potential.