Claudio Ranieri's side, who needed a remarkable late charge to avoid relegation last season, are flying high in second place and are now rated 11-10 for a top-four finish, compared to 200-1 in August according to British bookmaker William Hill.
Conversely, champions Chelsea were 7-4 favourites to retain their title but now, having sacked manager Jose Mourniho and languishing in 14th place, they are 150-1. Their top-four ambitions, initially a 1-33 shot, are now rated 10-1.
League leaders Arsenal and Manchester City are 11-8 joint favourites (from 7-2 and 3-1) to win the Premier League with Tottenham Hotspur at 8-1 to take the honours for the first time since 1961, from 150-1 at the start of the season.
At the foot of the table Aston Villa are 1-16 for relegation, compared to 5-2 pre-season.
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Premier League winner odds at the start of the season: 7-4 Chelsea; 3-1 Manchester City; 7-2 Arsenal; 5-1 Manchester United; 28-1 Liverpool; 150-1 Tottenham; 300-1 Everton; 300-1 Southampton; 3000-1 Crystal Palace; 3000-1 West Ham; 5000-1 Aston Villa; 5000-1 Leicester; 5000-1 Sunderland; 5000-1 West Brom; 7500-1 Bournemouth; 7500-1 Norwich; 10,000-1 Watford
Premier League relegation odds at the start of the season: 8-13 Watford; 1-1 Norwich; 6-5 Bournemouth; 2-1 Sunderland; 5-2 Aston Villa; 11-4 Leicester; 9-2 Newcastle; 9-2 West Brom; 6-1 Crystal Palace; 6-1 West Ham; 8-1 Swansea; 12-1 Stoke; 40-1 Everton; 40-1 Southampton; 250-1-Liverpool; 250-1 Tottenham; 1000-1 Arsenal; 1000-1 Chelsea; 1000-1 Man City; 1000-1 Man United.
Top four odds at the start of the season: 1-6 Arsenal; 1-16 Manchester City; 7-1 Tottenham; 200-1 Leicester; 1-5 United; 9-4 Liverpool; 1-33 Chelsea
Premier League winners on Jan 1: 11-8 Arsenal; 11-8 Manchester City; 8-1 Tottenham; 14-1 Leicester; 25-1 Manchester United; 33-1 Liverpool; 150-1 Chelsea; 250-1 Crystal Palace; 500-1 Everton
Premier League relegation Jan 1: 1-16 Aston Villa; 1-7 Sunderland; 10-11 Newcastle; 11-4 Norwich; 7-2 Bournemouth; 4-1 Swansea; 6-1 West Brom; 40-1 Watford; 40-1 West Ham; 50-1 Southampton; 66-1 Chelsea; 80-1 Stoke.
Top four Jan 1: 1-20 Arsenal; 1-20 Manchester City; 1-2 Tottenham; 11-10 Leicester; 5-4 Manchester United; 6-4 Liverpool; 10-1 Chelsea; 10-1 Crystal Palace; 20-1 Everton; 25-1 Stoke; 33-1 Southampton.
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