Remaining tickets for the visit of the Toffees on May 7- where the Foxes could win the Barclays Premier League title - sold out in 90 minutes on Monday
Claudio Ranieri's side need three wins from their final five games to seal a stunning title success after being 5000/1 outsiders at the start of the season
Season tickets sold out last May with the club setting a cap of 23,000 in the 32,500 capacity King Power Stadium.
Leicester also have tiered memberships available - with Family and Gold holders getting first priority on home tickets, with Silver and City members next in line - but membership does not guarantee a ticket.
After the match sold out, one online retailer was selling single tickets for £7,869.14 on Tuesday morning.
"Demand was higher for City's final home match and penultimate league fixture of an extraordinary campaign, with the vast majority of Gold and Family Fox Members able to secure their seat," said a club spokesman.
"The unauthorised sale of football tickets is a criminal offence under UK law
Leicester City Football Club will take action against any ticket touting or any attempt to resell tickets for above their face value.
"We encourage all supporters to report any such activity to the Club."
Supporters' club chairman Cliff Ginnetta also said fans were aware of the situation at the start of the season and while he sympathised with those who missed out, he believes the club are not to blame
"It was made clear at the start of the season, we had a meeting with the football club and they explained to everyone about everything. It was always going to be tight," he told Press Association Sport.
"I can understand people getting upset now but it's supply and demand and the demand is full
There are people I have known for years and last year they were taking the mick and saying they weren't going to pay to see them because they're rubbish and now they want a ticket
"It'll be the same people if the Tigers get to the (rugby European Cup) final.
"It's not only been the camaraderie with the staff and the players, it's been with the fans since we were in League One
That has swept the club along and there's a real hardcore of fans and the club have been loyal to them."
But some supporters, on the club's official Facebook page, have complained about being unable to get a ticket for the potentially historic match
Phillip Goodchild wrote: "Gutted. You would have thought paying £40 per season would get you a ticket. The club should have capped the memberships at the beginning of the season."
Adie Wheat said: "Gutted.been all season.1968 my first game never miss a season.silver member cant get a ticket for the most important game winning the league."
David Lea added: "Very bad when they are on ticket sites at anything from £495 to £5000
Who's giving the touts these tickets? What's the point of being a gold/silver member? I'd like to hear the clubs views on this."
Source: PA