In 2016 Philips had left Bolton's academy where his father, Jimmy, former professional, was director. Nat was on his way to the US after he secured a scholarship at the University of North Carolina. A couple of days before his planned flight to the United States, he joined Liverpool's academy instead. Phillips picks up the story with the Liverpool Echo: "It was a weird one. At Bolton, it didn't look like I was going to get anything at the end of that season. So I'd started to make plans, I was still doing my A-levels at school and had lined up a scholarship in America to go out there, hopefully, get a degree and get on that pathway to the MLS through the draft. That was all set up. I'd done a few days training at Huddersfield through a coach who'd been at Bolton. three days into that I got a call from Liverpool saying: 'we're going to Germany for pre-season, we'd like you to come and train with us'. I leapt at the opportunity and from then on it was a bit surreal."
After battling an ankle injury in 2018/19, Phillips was offered a new contract in August 2019 and was then subsequently loaned to Stuttgart of Bundesliga 2 in Germany to gain further experience. After Liverpool lost two out of four centre-halves in the first team to injury in the middle of the 2019/20 campaign, Liverpool recalled Phillips during the German winter break. He played the full ninety minutes of the FA Cup third round win over Everton, but returned to Stuttgart prior to the fourth round as other players came back to fitness. The Covid 19 pandemic meant he stayed there longer than expected, as the season didn't finish until the end of June, but it was a success as they were promoted back to the top flight.
Phillips was then expected to leave Liverpool during the transfer window but no deals were forthcoming. An injury crisis then led to him making his league debut against West Ham on 31st October, in which he put in a composed performance. He made two more appearances before Christmas then in the second half of the season an injury to Joel Matip gave him more opportunities. Phillips finished the season with seventeen league appearances and scored one goal. Prior to 2021/22 he signed a new contract, but accepted where his place was in the squad indicating he was ready to help out whenever required.