Klopp was with Borussia Dortmund when he met with United directors to discuss a move to Old Trafford.
Speaking on the Diary of a CEO podcast, Klopp admits meeting with United officials after David Moyes' dismissal in 2014.
"It's difficult, we're not in a private space but there are some reasons but the people in that conversation that I didn't like," he said. "So, United was that big 'we get all the players we want, we get him, we get him, we get him' and I was sitting there like 'huh?'.
"It was not my project, it didn't feel like my project, it was the wrong time but on top of that, it was not my project. I didn't want to bring back (Paul) Pogba, Pogba is a sensational player my God, but these things don't work usually.
"Or Cristiano (Ronaldo) my God we all know he's the best player in the world together with (Lionel) Messi. Bringing him back never helps, in that time in 2013, it was not about Cristiano, maybe Paul I'm not sure but the idea was, 'we bring the best players together then let's go'.
"Not at all (about the football) then I sat there like it wasn't for me. Then the pure football project comes up and a sensational talk to Mike Gordon (Fenway Sports Group president) that's really important as well.
"He's the owner but John (Henry) and Tom (Werner), after the talk I wanted to be Mike's friend, he was such a nice guy. After that, it was pretty special."
Indeed, a year later Klopp, now global football chief for Red Bull, was named Liverpool manager after the departure of Brendan Rogers.