Phil Neville has challenged Everton to achieve their highest league finish since they last won the title in 1987.
Neville believes his side are capable of catching Chelsea and Manchester City to take second place this season.
David Moyes' side missed the chance to close the gap on fourth-placed Tottenham as they were held 0-0 by Swansea at Goodison Park on Saturday.
That result has left Everton in fifth, three points adrift of Spurs, who currently occupy the fourth and final Champions League qualification spot.
Manager Moyes and captain Neville both believe that their side are playing well enough to aim higher than fourth, however.
And Neville reckons that Everton should be aiming to close an 11-point gap on defending champions City to claim second spot.
The Merseysiders have not finished higher than fourth since doing so in the old First Division under Howard Kendall 26 years ago.
But Neville, 35, told the Liverpool Daily Post: "We need to keep believing and thinking like that, it is the only way to be.
"We want to finish in the top four, and not just fourth. We want to catch Chelsea and Man City.
"We have got to keep aiming high, not waiting for teams to catch us up. We can't look behind us. We have got to be positive, look forward to the next games.
"Every game in the Premier League in the next month or two is going to be really difficult. It is that time of year, the pitches are getting softer, a bit bobblier and the weather is cold. It is about digging out results rather than playing fantastic football."
Moyes, meanwhile, reckons Everton are playing well enough to make a good push for third place. His side have lost only three out of 22 league games this season - the same number as leaders Manchester United.
However, Everton have been held back by 10 draws, nine more than the leaders.
Moyes said: "We have played well enough to be aiming for third place. Sometimes, you have to find ways of winning when it doesn't go for you, and maybe that is where we are beginning to feel we are a little bit short."