31-year-old winger Downing was sold to West Ham United in the summer of 2013 having spent two seasons at Anfield, the second of which was under Rodgers.
"I had a fall out with the manager in the second year when I didn't play," said Downing.
"When Brendan came in, for me he wanted his own players from day one I could sense that.
"We had our ups and downs early on. I told him how I felt and he said the same to me. We didn't get on.
"I was out of the team and it was October, I was going to leave but Brendan was never going to allow that. I think he'd rather me sat there doing nothing which is a bit strange.
"The team wasn't doing well so I kept my head down and when we had a few injuries he put me in at left-back. It was strange for me but I enjoyed it. I had a lot of the ball, you don't have to defend as much playing for Liverpool because they have a lot of the ball.
"Come the end of the season I was a regular playing as a right winger, I really enjoyed playing with Suarez, Sturridge and Coutinho. What's not to enjoy? I finished the season quite well so it was strange to leave in the summer."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!