Everton manager Roberto Martinez has still not given up hope of sneaking into the Champions League as his side enter the last-chance saloon.
While a point at home to title-chasing Manchester City will guarantee a return to European football next season it would almost certainly end their already-slim top-four challenge.
Arsenal, who play Sunday, are four points ahead with a superior but not insurmountable goal difference advantage but Arsene Wenger's side need to drop four points in their last two matches for Everton to stand a chance of catching them.
The Toffees look like being the unlucky losers as their points tally of 69 would have qualified them for the Champions League in seven of the last 11 seasons.
But that does not mean Martinez is conceding defeat or happy to settle for a point which will secure a Europa League spot.
"We don't look at it that way. We have 69 points and we want to beat that. We don't take it lightly," he said.
"We need six points because I still think 75 points will be very much an exceptional figure, wherever it takes you.
"The only thing you can control in football is what you can do.
"Seventy-five points in the last three seasons would have got you in the top three.
"We are not a team who are happy just to do enough, that is not in our nature. "
City will arrive knowing they almost certainly need all three points to retain their narrow edge over Liverpool in the title race.
But Everton have won their last four matches at home to City and have lost only twice in the league at Goodison Park since December 30 2012.
Martinez takes great confidence from that and wants his side to give the fans a good send off in the final home game of what has been a successful season of transition after the departure of David Moyes last summer.
"This is one of those glamorous games you keep in your memory forever," he added.
"We have been outstanding in the last few fixtures at home and you look at (wins against) similar teams like Arsenal and Manchester United and we need to carry on at the same level.
"It is important we give our fans a proper send off and make it a performance to remember.
"It is a very easy game to approach from our point of view.
"The last home fixture is always a special fixture so in that respect it is very easy - we are fully focused on hosting a really important game. "
Playmaker David Silva could return for title favourites Manchester City.
The Spaniard missed last weekend's win at Crystal Palace after being carried off on a stretcher with an ankle injury in the previous game against West Brom.
The 28-year-old has now recovered and his availability gives City a lift ahead of the final week of the season.
Manager Manuel Pellegrini said: "David is a very important player for us. He will be in the squad list.
"The only player we have injured is Jesus Navas. All the rest of the squad are fit."
Winger Navas has missed the last three games with an ankle injury.
City, in third, trail leaders Liverpool by three points but still have three games to play as opposed to their rivals' two - and have a superior goal difference.
They play the first of them at Goodison Park this weekend before concluding their campaign with home matches against Aston Villa and West Ham.
Pellegrini expects Everton, who still have an outside chance of qualifying for the Champions League, to provide tough opposition.
Pellegrini said: "I think Everton at any stage of the season will always be a difficult team. They play very well, Roberto (Martinez) is doing a very good job there, the same way he did before at Wigan.
"He is playing for Champions League, Europa League.
"We don't expect anything at Everton. We're sure we are going to have a very tough game there."
Victory for Everton could hand the title initiative to their fiercest rivals Liverpool - something their fans may not relish - but Pellegrini does not think that will affect the players' mentality.
He said: "The feeling outside will not decide the match. I think the Everton players will try to win the game."
Pellegrini added that defender Matija Nastasic is back in full training after three months out with a knee injury but is not match-fit.
He said: "Nastasic is working with the squad but he is not able to play in this moment. He's not injured any more."