Foxes boss Brendan Rodgers is prepared to leave the duo out to give them time to recover from injuries.
Striker Vardy has a long-term hip problem while Maddison picked up a knee injury at the win at Newcastle.
Leicester go to the bet365 Stadium in the third round on Saturday but Rodgers is likely to be without his star men.
He said: "Our two question marks will be with Jamie Vardy and James Maddison. Both of those players have done really well to get through these last number of games because they've been carrying some injuries.
"This may be an opportunity for us to let them recover and then be ready after the weekend, as both players haven't trained this week.
"It's primarily that they've got issues, Jamie obviously around his hip and groin area and James with his knee, so because of the games and the closeness of the games, they haven't been able to have the recovery and rest period.
"This would allow it to settle right down, so we're having to look at where we can do that, for the benefit of the short and the longer term.
"So this is probably going to be the weekend where they miss out which will get them ready again for the games after that."
Caglar Soyuncu is fit after a groin issue while Ricardo Pereira is out but has returned to training after his own groin injury.
Meanwhile, Demarai Gray and Islam Slimani can leave if the right offer comes in this month.
Winger Gray, 24, joined the Foxes from Birmingham in 2016 and helped them win the Premier League while 32-year-old striker Slimani joined for a then club-record £29million the summer after the club won the title.
Rodgers added: "They have trained really well but both recognise and feel the need to get game time elsewhere. They are of the age where they want to be first-team regulars. They have the chance to explore that."
Hamza Choudhury could also leave the King Power Stadium this month with Newcastle and West Brom reportedly keen on the midfielder.
"There have been one or two clubs (asking about Choudhury). He is not necessarily a player we want to let out on loan," added Rodgers.
"He has played quite a number of games for me this season but he's at the stage where he wants to play more.
"There have been enquiries and we'll look at it over the course of January."