Having already brought in Ben White and Albert Sambi Lokonga, Arsenal are rumored to be interested in the Leicester midfielder, though Rodgers dismissed those reports on Thursday.
Leicester, who are preparing for the Community Shield on Saturday, won the FA Cup last season before falling at the final hurdle for Champions League qualification, with Maddison playing an integral role.
"Yes, I believe so," Rodgers said when asked whether Maddison would remain at the King Power Stadium. "I haven't been told anything to say he won't be.
"He's happy in training, he's working very hard and he's just recently become a father so he has responsibility off the pitch as well.
"There's obviously gossip and speculation that goes around, especially this time of year, but James is a very important member of our squad.
"He's a very talented player. His season was disrupted last year by injury but hopefully this season he can go and show what a top player he is.”
Maddison, whose 13 goal involvements in 31 games last term represented his best return in the Premier League, led Leicester's charts for chances created with 51, despite playing seven games fewer than second-placed Youri Tielemans.
The England midfielder's 788 passes inside the opposition half were the second most among Rodgers' players, yet Maddison still ranked fourth with 81.22 per cent of those balls finding a team-mate.
While Rodgers will have reason to celebrate if he can keep a hold of playmaker Maddison, Wednesday's friendly against Villarreal led to concerning issues at the back.
Wesley Fofana, who was just one of two defenders to attempt at least 50 tackles, make 50 interceptions and produce 50 headed clearances last season, suffered a broken leg against the LaLiga outfit, leaving Leicester short for centre-backs.
Rodgers admitted he was "not overly happy with the way the game was officiated" and concluded it was "disappointing for something like that to happen in a pre-season friendly".
Already without the injured Jonny Evans, Leicester have just Caglar Soyuncu left as a first-choice centre-half and could be forced to push Wilfred Ndidi back into defence for Saturday's clash with Manchester City.
Rodgers now faces a race against the clock to fill the defensive void as he noted the shock 2015-16 Premier League winners are "definitely light in that area."