The winger played for Klopp for one season before being sold to Bournemouth in 2016 for £15m.
"He came in, and obviously, he's gonna want to have his own players," Ibe recalled on the Sports Agents podcast
"We had a conversation, and it was good at first, but I don't really think he honoured it. Young players, I've noticed, or even players in general, they'll hear something from their manager or whoever, and they'll be scared to ruin their manager's reputation.
"The conversations that we had when he first came because he was really happy with how I was playing because I was either starting a game or, if I was not starting, I was the first on.
"He always had this thing of when I was playing well, he would slap the back of my head. He was really happy with me and wanted me to take this into the new season, and then that changed because they signed a new player and we weren't the same story then."
Asked if he tried again to speak with Klopp, Ibe added: "I did, but the response was 'I think it's best you leave.'"