At the beginning of the season, Claudio Ranieri's side were as much as 5,000-1 to finish as champions, while the odds were 1000-1 to be top at Christmas.
The Foxes lead the Premier League by five points from Tottenham and have lost just three times all season.
Leicester can guarantee themselves a shock title triumph with three wins from their remaining four games.
Betfred are the only bookmakers to have already paid out on Leicester as champions, after they beat Southampton 1-0 on 3 April.
"I've been wrong before but this time I can't see Spurs or Arsenal catching Ranieri's men," said Betfred boss Fred Done.
At the start of the season, 47 people placed a bet with Ladbrokes for Leicester to win the title at 5000-1 - of which 23 have cashed out, while 24 are still awaiting their fate.
"Leicester's win would be the biggest upset in the history of betting," Alex Donohue of Ladbrokes told BBC Sport. "It would be the worst result for us financially and our biggest payout by a distance.
"If Chelsea, Manchester City or Manchester United would have won, the total payouts would have been in the few hundred thousands.
"Leicester have been upsetting the odds all season but it is a brilliant Hollywood story that we are a part of. Hats off to anyone who backed them at the start of the season."
Last month, a Leicester fan cashed out for £72,000 from a £50 bet on his team to win the title.
The UK's leading bookmakers face paying out more than £10m if Leicester City win the Premier League title.