The Reds academy graduate was released by the Cherries last month after a disappointing four-year spell.
"I had a chat with Klopp, and he thought it was best for me to spread my wings," Ibe told The Beautiful Game podcast.
"We put it in the contract that, within the first three seasons, there was a buy-back clause.
"I went thinking I needed more time on the pitch, cause he was bringing Sadio Mane and then the following season he brought in Mo Salah.
"So I just thought that I needed to change clubs and become the main man there."