There is expected to be a summer exodus at the King Power Stadium after the Foxes were relegated to the Championship.
A number of players are out of contract at the end of the season, including Jonny Evans, Ryan Bertrand and Youri Tielemans.
Caglar Soyuncu will also leave the club when his contract expires, and he is widely expected to sign for Spanish club Atletico Madrid on a free transfer.
Leicester are also expected to lose Maddison and Barnes, who are both attracting interest from top Premier League clubs.
According to The Sun, Tottenham and Newcastle are both pushing hard to sign the Leicester pair this summer.
The report claims that Maddison and Barnes will command fees of around £40m, but the Foxes are hopeful that a bidding war could drive up that price.
Leicester would rather agree quick sales, and put the funds into their summer transfer budget as they look to build a squad that can win promotion straight back to the Premier League.
Newcastle are wary of staying within Financial Fair Play rules, but they would be able to offer the duo Champions League football after finishing in fourth place.
In contrast, Tottenham finished the 2022-23 campaign in eighth position and missed out on European football altogether.
Maddison, who is set to enter the final 12 months of his contract, has also been linked with a move to Arsenal.
A recent report claimed that the Gunners and their North London rivals, Tottenham, are the front-runners in the race to sign Maddison.
Barnes, meanwhile, is believed to be keen on completing a move to Newcastle, with the 25-year-old looking to play Champions League football.
Maddison has scored 55 goals in 203 games for the Foxes, while Barnes has registered 45 goals in 187 Leicester appearances.