Tickets to the Foxes' penultimate game of the season sold out within 90 minutes after going on sale following "unprecedented demand" according to a club spokesperson.
Soon after a pair appeared on secondary ticket websites for as much as £15,000 while other tickets were being listed for £3,000.
Claudio Ranieri's side need to win just three of their remaining five games to secure the Premier League title, meaning they could be confirmed champions by the time Everton come to visit on Saturday 7 May.
A statement on the club website claimed that "demand was higher than ever" as fans attempt to secure their seat at the 32,212 capacity stadium.
However, those fans lucky enough to gain entry have been warned against cashing in through unauthorised avenues.
A spokesperson said: "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."