Champions League qualification may be the limit of their ambitions this season after defeat at Tottenham on Sunday left the Toffees five points adrift of fourth-placed Liverpool, but that will not stop Martinez dreaming bigger.
"Obviously it seems no one wants to win the league," said the Spaniard.
"No one wants to come out and say they want to win the league - we are quite happy to want to win the league!
"I think it will be an interesting run from now until the end of the season.
"There are many aspects which will have an effect: playing in Europe, how domestically the cup pans out.
"Clearly this is an exciting moment of the season; you are working for two thirds of the season to try to get yourself a position to fight for your aim and everything will be decided over the next 12 to 13 weeks.
"This league never stops surprising. A couple of years back you saw a big gap at the top of eight points cut down in a shorter period than this.
"There are many points to play for. What is really exciting is the moment of form that the team is starting to get.
"You look throughout the league - fighting for the top, fighting for the Champions League, fighting against relegation - and it is the closest it has been for a long time."
Martinez also waded into the argument over retrospective discipline for players after Manchester City midfielder Yaya Toure on Tuesday escaped punishment despite appearing to aim a kick at Norwich striker Ricky van Wolfswinkel - prompting Chelsea boss Jose Mourinho to claim it gave free rein to players.
"It is not just in that incident, I think in general I am not a big believer of going back to every single game and refereeing it because it would be impossible," said Martinez.
"I think there is a thin line. Clearly the players can't get away with everything, any wrong behaviour should be spotted, but you want that to be done on the day.
"You can look into every single aspect that can give as much help as we can to referees because it is one of the hardest jobs in the game but we shouldn't take things out of context.
"We should have some common sense in helping the referees as much as we can."
Comments from Everton's on-loan striker Romelu Lukaku suggest he will not be hanging around if the Toffees do not make it into the top four by the end of the season.
Earlier in the campaign, with the club inside the top four, the 20-year-old suggested would be prepared to stay at Goodison Park if Champions League football was on offer.
That seemed fanciful as even if they did qualify it would be doubtful whether they would be able to afford his transfer fee even if Chelsea were prepared to sell.
Lukaku now appears to have turned his attention back to his parent club, who are the current league leaders.
"It's time for me to play Champions League and that's what I want,' he told Belgian newspaper Het Laatste Nieuws.
"When I turn 21 (in May) I'll have been a professional for five years, I need this in my evolution.
"Cristiano Ronaldo and Wayne Rooney were already in the Champions League when they were 23 or 24.
"I don't want to play my first games in the Champions League when I'm 23, I want it now. I have to show now that I'm ready. I'm still young but I've no time to waste.
"I want to be a top player and I also think I can shout that out.
"I've scored a lot of goals but I haven't won many titles or cups yet. I want to win something.
"I still have two years on my contract in Chelsea and I know they're tracking my evolution. In the end, it's up to the manager (Jose Mourinho) to decide."