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Quansah, 22, has only started seven games for the Reds since the turn of the year, the last five of which have been defeats.
The defender made his breakthrough last season under Jurgen Klopp and new manager Arne Slot gave him a start in his very first game at newly-promoted Ipswich Town in August.
In anticipation of Trent Alexander-Arnold's exit, the Reds have agreed a deal to sign right-back Jeremie Frimpong on a five-year contract after informing Bayer Leverkusen that they plan to pay his £29.5million release clause.
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Right-back is a position that Quansah, a central defender by trade, has featured regularly in under Slot.
"Ibou [Konate] and Virgil [van Dijk] were and are such a strong combination that he didn't play a lot," Slot acknowledged in March after his latest England call-up.
"But every time he had to play, except for maybe the first one or two games, but afterwards he had to play you could see that maybe he is no longer a talent because as a talent you don't have any setbacks, but the moment you get setbacks it's about you and how you react.
I think he showed in his recent performances that he's outgrown being called a talent.
Should Liverpool sell Jarell Quansah?
He did really well the last few times he had to play for us and even in a position he's not completely used to as a right full-back.
"But in my opinion, he has also the qualities to play in that position.
He's strong, he's fast, he's very comfortable with the ball and it gives us an extra quality if we play him, which we saw [against Paris Saint-Germain], in terms of set-pieces because he was the one that was this far away from us qualifying for the next round by heading the ball onto the post, because that one was not offside.
"He showed mentality and that he had quality.