Fofana is keen to join Thomas Tuchel's side and missed one training session last week in order to force a move.
Fofana was left out of the squad that lost 2-1 at home to Southampton over the weekend and was again missing in action in Tuesday's League Cup encounter at Stockport, where the Foxes prevailed on penalties after a goalless draw.
Including add-ons, Chelsea are prepared to pay up to £70m to bring Fofana to Stamford Bridge but Leicester insist the Frenchman is not for sale.
"There was an offer gone in and it's been rejected," manager Brendan Rodgers said in a press conference after Tuesday's game.
"Apart from that, I'm not 100 per cent on the other details, because we were focusing on the game [against Stockport].
"He's training with the under-23s so he can get his football fitness and keep working. It's so important at this stage to control any sort of distractions that may be there.
"He's a good kid, it's just been a really challenging situation for him. I've had it a number of times in my career where there's players who can deal with it, cope with it, get on, want to help their team-mates. There's others that just can’t deal with the distraction.
"Of course that distracts them and it's not quite right, and they miss a training session, then you need the full commitment from your players. These guys get well paid. The very least you can do is turn up. And if you don't, with all due respect, you can’t then just think you can walk into our group."
Fofana only signed a new contract until 2027 with Leicester back in March after returning from a long-term knee injury that restricted him to just 12 appearances last season.
The 21-year-old was one of the revelations of the 2020/2021 season following a summer move from Saint Etienne as he made 38 appearances across all competitions to help Leicester win the FA Cup and finish fifth in the Premier League.
