The McNeill family went public at the weekend to reveal the heartache of his long battle with dementia and their desire for more research into the effects of repeatedly heading a ball.
Rodgers was aware of his condition and has revealed his sadness over a figure he revered in his youth growing up in Northern Ireland.
The Celtic manager said: “It’s clearly sad, the news that has come out. I saw him last at Celtic v Aberdeen.
“He’s certainly in the thoughts of every Celtic supporter, every person who works here.”
Rodgers added: “He is one of the true great legends of the club. A real icon of Celtic.
“He led the greatest ever team. He was an incredible player and went on to be a real successful manager, too.
McNeill, of course, famously led Celtic to the European Cup in Lisbon in 1967 but in an extraordinary career as a player and twice as manager he was involved in 31 of Celtic’s 100 major trophy victories.
Rodgers said: “It’s remarkable, there are very few figures who really inspire generations of people. You look at Jock Stein and what he did, and Billy is one of those.
“They can inspire younger ones because the legend will never fade away. When I was a young guy growing up I was fed the stories of 1967 and I was then old enough to remember the 1980s and beyond.
“These figures are prevalent in your upbringing. And then you get the chance to meet them.
“It’s like me seeing Danny McGrain here every day. I can’t believe I’m talking to him and thinking, “what would my dad think?”
“When I met Billy McNeill I just thought of my uncles and all my family and I went into a dream. It’s the same with obby Lennox, Stevie Chalmers and the rest – that never ever goes away.
“For the younger players this is the reason they are here. That’s why when I first came in, I asked them to defend the culture of the club because these are the guys who created it.”
Rodgers, preparing for tomorrow night’s league match in Inverness, believes the history of Celtic is not a hindrance but something to be embraced.
He said: “It was the same at Liverpool. I was never frightened of the past as it was one of the big reasons I went to Liverpool – because of the great history of the club. I wanted to create new history.
“Coming to Celtic I knew in a lot more depth the history of the club being a supporter. That aspect is still very strong in my thinking. “I have to make sure we measure up to the standards these guys created.
“When I sit with John Clark and have a cup of tea after training or meet some of the other guys, you only have to spend a short bit of time with them and they give you little bits of gold dust.
“These were guys who weren’t playing for the money. They were playing for the love of football and the love of the club. The game was still the game back then.
“I always find the time for these guys. We are here because of them.”
The NFL investigated the correlation between repeated concussions in American football and brain problems, and Rodgers would like to see more work done on the damage that heading a football may cause.
He added: “It’s an investigation where it would be very worth seeing what the findings are. You can’t ignore the heavy balls they used in the 1960s and 1970s. We’ve seen the balls in the museums with the big laces on them. So it would be worth getting the findings of the research. And if the McNeill family is open to that, then that’s a good step.”