The 23-year-old featured sporadically during 2016/17 with a serious injury ending his campaign prematurely.
Stewart, looking beyond the summer, is aiming to become an invaluable member of Klopp’s first team squad as the Reds are set to fight on four fronts.
“Trying to break through, trying to stay fit and trying to be ready for when I’m called upon [is my aim],” he told the club’s official website.
“Next season there are going to be a lot of games, especially if we qualify for the Champions League, so I just want to keep fit in the summer, work hard and then see where the season takes us.
“That’s the thing that keeps me going – I’ve done it before, so I know it’s possible.
“I see the players I train with and they’re amazing players I’m competing with and playing with, but I will keep believing because I’ve been through it before.”
Nominally a defensive midfielder Stewart, a former Tottenham Hotspur academy graduate, is capable of playing in central defence or at left-back.
To date he’s featured across 20 matches for the Reds, all of which coming under Klopp, since debuting against Exeter City in January 2016.
Recently the London-born footballer was linked with a move to newly promoted Premier League side Brighton, but Liverpool are reluctant to see him go, especially as having squad depth is vital next season.
Stewart, who joined the Reds in 2014 on a free transfer, current deal expires in June 2021 having signed an extension last November.