Brendan Rodgers' Reds are paying $1.75 at bet365 to beat the Toffees at Anfield, with Roberto Martinez's men at $4.33 and the draw worth $3.75.
The hosts would appear a little short given both teams drew their last league fixture and just one point separates fourth-place Liverpool from Everton in sixth spot.
With that in mind, perhaps it's worth backing a draw at half-time and a Liverpool win at a healthy $5.00 in the half-time/full-time market.
|Go for a half-time draw and Liverpool win at $5.00
Elsewhere on Wednesday morning, United are $1.25 favourites to dispatch Cardiff City ($11.00) at Old Trafford, where the draw is at $5.75.
Juan Mata could be in line for his United debut after completing a reported 37 million-pound switch from Chelsea and the Spaniard is at something of an optimistic $7.50 to open the scoring on his first start in a red shirt.
Arsenal are also fancied despite being away from home. You can get only $1.90 on a Gunners win at Southampton, who are paying $3.80, with draw at $3.60.
Harder for punters to call is Crystal Palace ($2.40) at home to Hull City ($3.10) and Newcastle United ($2.37) away to Norwich City ($2.87), with the draw paying $3.10 and $3.40 respectively in those two games.
Finally, struggling Fulham ($5.00) are being given little chances of winning away to Swansea City ($1.66), with the draw in that one at $3.75.