The 25-year-old midfielder has two years left on his current deal but has attracted interest this summer from Newcastle, who failed to prise him away in a £40million bid.
Maddison is one of the Foxes' star players and the club are keen to avoid him entering the final year of his contract next summer.
Asked whether there had been dialogue between the two parties, Rodgers said: "I believe so, I believe they've spoken. Yeah, Jon (Rudkin, director of football) has spoken to them a number of times, yes.
"I'm pretty sure the club would want to do that (tie him down). Both sides have to be able to find an agreement.
"With James, with two years left, naturally the club would want to protect the asset. But it works both ways.
"Sometimes, everything goes onto the club. If a player, I'm not saying James, doesn't want to sign it, then it can be a stalemate.
"But absolutely, he's an outstanding player and of course, Leicester City would benefit from keeping him longer."
Maddison, who will have an eye on earning a place in England's World Cup squad, has started the season well for the Foxes and Rodgers says there has been no change in him following the interest from Newcastle.
"He's been brilliant. He's a top-class player. Arsenal, in the spells, where he had the ball, he looked the most dangerous player," he said.
"He scored a very good goal. For me, James is still the same. He's improving, developing, and happy.
"Of course, he's a top player at this level, so people will be interested in him, but I've seen no change in him whatsoever."
Rodgers also expects Wesley Fofana to still be at the club after the transfer window shuts.
The defender has been the subject of two bids from Chelsea but both were rejected and nothing fresh has arrived in the last 10 days.
Rodgers has insisted all along that Fofana is not for sale and does not expect to lose him in the next fortnight.
"I don't think so far ahead, the idea is that he is a Leicester City player, " he said.
"He is not for sale, the club have made that clear, unless anything changes on that I would expect him to be here.
"Currently at this moment there is nothing new and nothing has changed from when we last spoke."
There were reports the 21-year-old had asked Leicester to accept a lower fee while Rodgers has denied the player handed in a transfer request.
Asked to clear up the speculation, the boss added: "Yes, I can, he hasn't. He's a great kid. He's loved by his team-mates.
"He's a great personality. He's still developing. He's nowhere near the finished article.
"We've spoken numbers of times about the whole situation and of course a private conversation. Our communication is normal, and we just continue to prepare for the games.
"It's a challenge for any player and for clubs around this time when the window is open, and there's lots of speculation and lots of noise that goes on with it, and especially for a young player - 21 - all the speculation that has surrounded it.
"That's why we're here, to help and educate him in dealing with all these rumours. The focus is very much on the team and getting them ready for the weekend."