Rodgers took Liverpool to the brink of their first Premier League title in 24 years in the 2013/14 season before losing out to Manchester City.
However, with star player Luis Suárez departing to Barcelona in the summer, Liverpool could only finish sixth the next season and finished it with a disastrous 6-1 defeat at Stoke City.
The Northern Irishman was eventually sacked in October 2015 with the Reds in tenth position after a stuttering start to the new campaign.
Milner joined just a few months before Rodgers was axed, but the former England midfielder still saw enough to convince him of his managerial talent.
Speaking to publicise A Match for Cancer at Celtic Park, Milner said:
My impression of him is that he's a very good manager. He was one of the main reasons I signed for Liverpool, in fact. It's a massive club and doesn't need too much selling but Brendan played a very big part when I made my decision.
It was unfortunate I didn't get to play under him for longer. That remains a disappointment but it's pleasing to me to see that he's come to another big club and done so well.
Liverpool's loss has been Celtic's gain, but we were lucky enough to bring in Jürgen Klopp after Brendan. He's another top manager, so it's worked out well for both clubs.
Liverpool are currently flourishing under Klopp, but Milner is confident Rodgers would have done similar if given more time at Anfield.
Brendan did well at Anfield and he came so close to ending that long wait for the title.
Would he have turned things round if he'd been given more time? I'm sure he would have done.
You don't come as close as he did to winning the league without doing something right, but the club chose a different path.