Leeds United's positive start to the season has seen them made 10th-favourite to get a top-four finish.
The Whites are still tipped to finish some way off the Champions League places, but their form, combined with odds of 12/1, may be enough to tempt some fans into an optimistic flutter.
Despite Leeds taking points off Manchester City and pushing Liverpool close, it appears the bookies think the big six stand the best chance of finishing in the top four this season.
Manchester United's poor start to the season sees them given odds of 9/4, which is still shorter than the Whites.
Everton's perfect start to the season sees them ranked as the seventh-favourite to take a Champions League spot.
Champions Liverpool are the lowest odds out of all the 20 teams, valued at 1/33, with Manchester City at 1/14.
Then it’s Chelsea, who like the Toffees, enjoyed a brilliant transfer window, are 1/2 to finish in the top four again.
Tottenham Hotspur are at 8/5, with Arsenal at 17/10 and Man United priced at 9/4, with Everton below them with a value of 12/5.
Below is the full list of teams most likely to finish in the top four, according to The Pools.
Liverpool: 1/33
Manchester City: 1/14
Chelsea: 1/2
Tottenham Hotspur: 8/5
Arsenal: 17/10
Manchester United: 9/4
Everton: 12/5
Leicester City: 17/4
Wolves: 17/2
Leeds United: 12/1
Aston Villa: 25/1
Southampton: 40/1
West Ham United: 66/1
Newcastle United: 100/1
Crystal Palace: 100/1
Brighton & Hove Albion: 125/1
Burnley: 200/1
Sheffield United: 200/1
West Bromwich Albion: 200/1
Fulham: 500/1
