The ex-Reds striker, who won the 2001 Ballon d'Or during his time at Anfield, was a free agent five years ago after leaving Newcastle United.
Owen was keen to secure a return to Anfield, and spoke to Liverpool centre-back Jamie Carragher about a comeback, but claimed that the club were not interested.
He told the club's official TV station: "I left Newcastle and the first thing I did was phone Carra to ask him to speak to the manager (Rafael Benitez).
"However, at that time Liverpool wasn't an option, they didn't want me. I tried my best to get back, but had to have a look out as to who wanted me and who was the best team to sign for.
"The three teams that were seriously in for me were Hull City, Everton and Manchester United. I could have gone to Hull I suppose, but in my mind I had to play at the best level possible. Liverpool didn't want me, so I signed for Manchester United."
Owen retired in 2013 after playing his final season with Stoke City.