Speculation over the summer suggested that the 22-year-old playmaker was attracting interest from afar.
Maddison was billed as a useful addition for Liverpool, as Jurgen Klopp looks to land another No.10, while those at Old Trafford are said to be readying an approach.
Leicester boss Rodgers concedes there is little he can do to curb the rumours or to prevent admiring glances from turning the heads of those on the books at the King Power Stadium.
Having already lost England international defender Harry Maguire to United in a record-breaking £80 million ($100m) deal, the Foxes manager said: “I don’t worry. It’s natural in the game, it’s going to happen.
“If you’re at one of the so-called top clubs, you’ll always look elsewhere for the best players, and when you’re a club like Leicester you’ll always be in danger of losing your top players. That’s football.
“All we can do is create an environment here for them to develop and improve and then if something happens in the future that’s out of your control, then that’s the way it works.
“I tend not to worry so much, I just focus on making them the best they can be and if they then move on, that’s how it works.
“But when they’re here, they give their best, give everything to the supporters and the club, and we’ll see where it takes us.”
Rodgers, who spent three years as Liverpool boss between 2012 and 2015, added on the lure of potential moves to Anfield or Old Trafford: “I’ve been fortunate that I’ve been at Liverpool where I understand the draw of that type of club.
“Liverpool and Manchester United are two of the biggest clubs by far. There’s other great clubs, there’s big clubs, but those two, in terms of worldwide status, are above the other clubs. There are other great clubs that are trying to catch them up but those two, in my experience, are a level above.
“So whenever a player gets an opportunity to go to a club like that, to experience that type of pressure, that expectation – and of course there’ll be a financial side to it as well, let’s be real – that as a package in a short career is maybe something that is too hard to turn down.
“I understand it, I get it. What we’re building here is exciting in how we’re trying to progress and with the new training ground and everything else, however, for lots of players, that draw is still there and I understand it.”
Maddison has continued to impress for Leicester this season, contributing one goal and two assists across six appearances, and was able to force his way back into the senior England squad for Euro 2020 qualifiers against Bulgaria and Kosovo.