The Leicester City boss has insisted that the key players will not be sold this summer.
Arsenal are currently in the market for an attacking midfielder and have been linked with an array of players.
Famed Italian Journalist Fabrizio Romano had earlier stated the Gunners cite Maddison as a perfect fit for their style of play.
The 24-year-old has been pivotal behind the Foxes’ resurgence over the last two seasons, racking up some impressive numbers in the process.
Rodgers said: “In conversations with the club, we don’t have to sell. That’s something that’s been made clear.
“The players want to stay. It’s a really exciting time at the club.
“There’s lots of gossip and speculation around, but I’m loving working with the guys here, they love being here, and we certainly have no need to sell. So I would suspect we’re looking to keep our best players.”
Leicester fell short of the Champions League qualification in the last two seasons, and Rodgers will be hoping to turn the fortunes around.
Elsewhere, Gunners have already made three signings, namely Nuno Tavares, Albert Sambi Lokonga and Ben White, with the latter becoming the club’s record transfer.
Martin Odegaard remains a target for the North Londoners. The Norwegian appears to have given the nod to return to Emirates Stadium, where he spent the final half of the last season on loan from Real Madrid.
Mikel Arteta has also confirmed that Granit Xhaka will remain at the club despite his exit speculations.