Joleon Lescott is hoping Everton can upset the Premier League 'elite' by pushing into the UEFA Champions League spots.
Everton are the only club to have broken the monopoly Manchester United, Chelsea, Arsenal and Liverpool have had on the top flight in the previous five seasons.
But, this term, Aston Villa are currently in fourth spot, while the Toffees are also trying to chase down the leading clubs.
Lescott says the Everton squad are not fazed by the so-called 'big four' and believes the stranglehold at the top can be loosened again.
"We don't like to use the term 'big four'," Lescott told Zoo magazine.
"All we want to do is get as high up the league as possible and if that means upsetting a supposed elite club, then all the better.
"It's tough to get up there, but it can be done. We did it a few years ago, so we have to keep doing our best."
Everton endured a fitful start to the season and Lescott feels the turning point was coming from behind to secure a 1-1 draw at home to champions United in October.
He added: "We've raised expectations recently at Goodison Park and it's true we dropped below those standards in the early part of the season and suffered for it.
"When we played Manchester United in October, we were getting beaten 1-0 at half-time, but came out in the second half and had a real go.
"The crowd could see the effort the team were putting in and they got right behind us to help get a 1-1 draw. Since then, we've kicked on nicely."
Manchester City have been tipped as long-term challengers for the Champions League places and Lescott, who has been linked with a move to Mark Hughes' side, is not concerned by the money at their disposal.
"At Everton, we're grateful for what we've got and can't do anything about other teams," continued Lescott. "We have to keep working hard.
"I get excited at the idea of Man City having billions. I'm like any fan - I like seeing the transfer gossip. So no, it doesn't bother me."
The full version of this interview is in ZOO magazine, out now.