"I remember spending time with Jurgen when he first got the job and I had left. We sat and we spoke," said Rodgers.
"Where was that? At Anfield?", asked Keys.
"No at my house," Rodgers replied to shocked laughter from the former Sky Sports presenters.
"Whatever help he needed as a manager I was there for that."
Rodgers was sacked as Liverpool manager after a torrid start to the Premier League season culminated in his dismissal in October.
The 43-year-old spoke about how he and Klopp and had discussed the fickle nature of the Premier League.
We talk about patience. An example is Robert Lewandowski at Bayern Munich and he wouldn’t have got the patience in the Premier League that he did in the Bundesliga and now look at him.
Rodgers' activity in the transfer market came under frequent scrutiny during his time at Anfield, spending almost £300m without delivering a trophy.
However Rodgers sought to defend his purchases, singling out Christian Benteke as a player who would eventually come good.
We felt at that time that Christian was up there in terms of goals to games. We felt that he was someone that we didn’t have in the squad. The problem now is the patience element. There doesn’t seem to be time.
Christian over time will show he's top class."
Liverpool lost their eighth game of the season in a 2-0 away defeat on Tuesday night leaving them eighth in the table, eleven points adrift of the Champions League places.
- Telegraph