The Toffees are due to visit Filbert Way on Wednesday for a 6pm GMT kick-off in a clash of two sides who will hope to challenge in the upper regions of the Premier League this season.
While Rodgers' managerial encounters with Ancelotti have been few and far between over the years, the Northern Irishman has been struck by both the Italian's experience and his sincerity.
In 2014, the current Foxes manager oversaw a Liverpool side against Ancelotti's Real Madrid in the UEFA Champions League, engaging in intriguing battles, both at Anfield and the Santiago Bernabéu.
He is excited to revisit those friendly rivalries at King Power Stadium this week as Leicester look to make it four wins in a row in all competitions ahead of a hectic festive run-in.
"His Real Madrid team was certainly very good!" Rodgers recalled on Tuesday. "They had won the Champions League the year beforehand. They were sensational that year.
'Carlo’s worked at the highest level. He’s worked with some top-class teams and he’s now at Everton, trying to impose his way of working there.
"He’s a really experienced manager, he’s a really good man. He’s got big experiences in his managerial career and it’s always really nice to see him.
"Carlo's a very humble man and he was obviously aware of me when I worked at Chelsea, so we had connections there.
"He’s a really great football man. I’ve had staff who have worked with me along the way that worked for him as well and he’s a really calming influence, especially around big players.
"He always has that humility and respect that he offers to people as well.
"When I spoke to him last, he said he was enjoying his time at Everton and his life up there in Merseyside as well, and he’s doing a very good job."
Rodgers can recall one instance, in the early summer of 2011, when he shared a taxi with Ancelotti ahead of the annual League Managers' Association award ceremony.
It took place just days before Rodgers' Swansea City were scheduled to face Reading at Wembley Stadium in the Championship Play-Off Final - and the former AC Milan manager's comments remain a fond memory.
"It was the week leading up to the play-off final and obviously he knew we were playing Reading and he knew it was one of my former clubs," the 47-year-old explained.
"He said: ‘You will definitely win the game because it is in the footballing gods!’ I only wish I was that confident at the time when he said it! His prediction came true.
"He was saying he’d had a similar experience, at a higher level, in a game between Juventus and AC Milan. Turns out, he can look into the future as well!"
Rodgers believes Everton will naturally benefit from the stature of a manager who has won divisional titles in England, Italy, France and Germany, alongside three UEFA Champions League triumphs.
Boosted by the summer arrivals of James Rodríguez, Allan and Abdoulaye Doucouré, among others, the Toffees are looking to be a more competitive force in the Premier League this term.
"He’s got that profile and will have respect as soon as he walks through the door with a lot of the players," the Leicester manager continued. "He has a lot of experiences which he can use to help the players.
"He’s also got Duncan [Ferguson] beside him as well, who’s a really influential figure there and has done a great job over a number of years at Everton.
"Between them and their staff and the players they’ve brought in, they’ve certainly improved and they’ll look to continue to, I’m sure.
"I look at them as being a really good team with some fantastic players. They are our next opponents, and we have to do everything we can to win."
Toffees striker Dominic Calvert-Lewin, on the other hand, is likely to pose a threat for the Foxes on Wednesday after netting 14 goals in all competitions this season.
Rodgers admits he has monitored the the 23-year-old's progress over recent campaigns and has backed him to follow in the footsteps of other Goodison Park favourites.
"The guys like Graeme Sharp, Duncan Ferguson, Gary Lineker, all those guys, they were terrific when they were there," the former Liverpool and Celtic manager added.
"I've got to say, I've been really, really impressed with him. I saw him a few years back as a young up and coming player and he had enthusiasm and strength.
"He's definitely, in the last 18 months, really added to his game. His athleticism is good, he's a willing boy, he can run in behind, he makes bright runs.
"Technically, he's really improved. When the ball comes into him, his set-up play's very good and he looks like he's very focused on getting goals.
"When it comes into him, he sets it, he gets into the box to get in and score, often off one touch, when he gets in there.
"I've seen big improvements in his game, which is a great testament to him, to want to improve, and I'm pretty sure the likes of Duncan will have been supporting him.
"Carlo's experience too [will aid his development further]. He's developing and still will continue to develop into a top-class striker."
City, meanwhile, headed into the midweek fixtures sitting third in the Premier League, one point adrift of the summit, after securing more league wins than any other side.
While Rodgers insists it is too soon to discuss possible achievements at the end of the campaign, the Northern Irishman does believe the table will be tighter than it was in 2019/20.
"With the nature of the league this season, with all the games and the compactness of the games, and the quality of the teams, it'll be tighter than it's been over the last few years," he said.
"There's still just a long way to go. All the teams who have been playing European football have got a period now, through until February, where they won't play too many games.
"Those teams might be a little bit fresher and whatnot, but it's been an interesting start and it's nice to be up there and around it. What Leicester showed in the 5,000/1 season is that everything is possible.
"It was one of the greatest stories in sport, but from that season, the odds have been dramatically cut on every team. It's been great to see the likes of Southampton, ourselves and West Ham up there.
"It's the job of every team to try and challenge and be up there for as long as you can."