Was the song "You'll Never Walk Alone" chosen as an anthem by Liverpool FC fans because it was a hit for Liverpool band Gerry and the Pacemakers?

Or did Gerry and the Pacemakers choose to record that song because it was already the anthem of Liverpool FC? The song was written in 1945 by Rodgers and Hammerstein for their musical "Carousel" and originally had nothing to do with Liverpool, but in 1963 Gerry and the Pacemakers covered the song and scored a massive hit with it. It was also around that time that Liverpool FC fans started singing it. Which came first?