Frimpong's arrival from Bayer Leverkusen was announced hours after Alexander-Arnold joined Real Madrid, with the Dutch international becoming Arne Slot's first signing since winning the English top flight.
"Liverpool. It's a big club, so it's big shoes regardless," Frimpong told Sky Sports in an interview published on Sunday, when asked if he would compete with Conor Bradley to succeed Alexander-Arnold as Liverpool's first choice for right back.
"It's a winning team ... they win trophies for a reason. If you play for a team like Liverpool you have to fill in the shoes and perform.
"I've always believed in myself. I'm a winner. That's what I'm going to bring to the team."
Amsterdam-born Frimpong, who can also play as a winger, spent nine years at Manchester City as a youth player before making his senior debut in 2019 at Celtic, who won the Scottish Premiership in his first season.
The 24-year-old joined Leverkusen in 2021 and made 34 appearances as they won the Bundesliga in 2023-24.
"The Premier League is the best league in the world. I grew up in Manchester so I always wanted to come back. It was always the plan," Frimpong said.
"I know what being a champion is like at Bayer Leverkusen, so joining a champion team is a privilege ... to go from watching (Liverpool) to playing for them is crazy.
"The manager has told me how I can help the team and he really likes me as a player. It's given me extra motivation and belief."