The neighbours meet at Anfield on Sunday, with sixth-place Everton five points ahead of seventh-place Liverpool and knowing a win will guarantee its status as the top club on Merseyside for a second straight season.
Outdoing Liverpool two years in succession has not happened for more than 50 years, however, and the job is far from done for Everton, with Liverpool holding an impressive home record against its oldest foe and buoyant after a 6-0 win at Newcastle last weekend.
Everton has not won at Anfield since 1999, while manager David Moyes has led his team to victory against Liverpool only three times in his 21 attempts.
"The fact that they haven't won at Anfield for so long has to play on their minds," Liverpool midfielder Stewart Downing said. "I am sure David Moyes will get right amongst them. He must be desperate to beat Liverpool. But we don't want that record to end. We did really well against Everton in the three games last season.
"We have to be ready and make sure we start well. It will be a good test for us and it will be tight with battles all over the pitch, but we're confident we can get another win."
Liverpool will look to close the gap to two points with two games to play but is without star striker Luis Suarez, who recently started a 10-match ban for biting an opponent.
"Derbies mean a lot and we know what's at stake," Everton midfielder Steven Pienaar said. "For the people of the city and the pride of the club, it's one of those games you don't want to lose.
"We will give everything to make sure we come away from Anfield with three points because it has been a long while since we won there."
A victory would not only give Everton the bragging rights for another season — it would also keep the club's faint hopes alive of qualifying for next season's Champions League as it bids to chase down Tottenham, Arsenal and Chelsea.
Third-place Chelsea qualified for the Europa League final by beating FC Basel on Thursday but finishing in the league's top four remains the priority and it faces a tough match against already crowned champion Manchester United on Sunday.
Chelsea manager Rafa Benitez has rotated the squad to keep his players as fresh as possible in the two competitions, with the team embarking on a hectic run-in that sees it play five games in 15 days. That includes a crunch match against fifth-place Tottenham on Wednesday.
"It is important to show this character and to keep winning and keep the momentum," Benitez said. "Hopefully we can do it. Man United will be tough, Tottenham will be crucial for us, so we know that we have difficult games but we have confidence and enough quality in the team so hopefully we can do well."
Fourth-place Arsenal can put pressure on Chelsea with a win on Saturday at Queens Park Rangers, which has already been relegated. Arsenal is one point behind Chelsea and two ahead of Tottenham but it has played a game more than both of its rivals.
Arsenal manager Arsene Wenger, who has endured a turbulent relationship with club supporters this season, dismissed speculation he might leave in the summer to join French team Paris Saint-Germain.
"I respect my contracts," Wenger said. "I want to stay (on past 2014) if I do well and if I consider or the club considers that I do well, that is all."
Tottenham forward Gareth Bale, who won the English Football Writers' Association's player of the year award on Thursday, is set to make his 200th appearance for Spurs when it hosts Southampton on Saturday.
Bale used to play for Southampton, coming through its youth team.
At the bottom, Wigan plays West Bromwich Albion as it tries to trim the five-point gap on fellow strugglers Newcastle, Aston Villa and Sunderland.
Newcastle is away to West Ham, Villa travels to Norwich and Sunderland is at home to Stoke on Monday.
Second-place Manchester City plays Swansea while Reading, which is the second team to have already been relegated, faces Fulham.