A fine run of form in recent weeks has propelled Athletic into sixth, just two points behind their opponents this weekend, and the Spain international hopes they can sustain their challenge in three competitions for the rest of the campaign.
He told Spanish news agency Efe: "The reality is we are where we are and why can't we qualify for the Champions League?
"This team is very ambitious and we always want to be as high in the table as we can.
"We are fighting in three competitions, we are still alive in the league, the Europa League and the Copa del Rey and from now on all the games are finals because if you lose one you can be out of the running in any one of them."
Marquez will return to the starting line-up after missing last weekend's 3-2 win at Rayo Vallecano through injury, along with Iker Muniain and Ander Herrera who were rested ahead of Tuesday's 2-1 win in the Copa del Rey semi-final first-leg at Mirandes. Oscar de Marcos also returns from suspension.
Fernando Llorente scored all of Athletic's goals in those two victories over the past week and Espanyol defender Raul Rodriguez admits they must be especially wary of the Spain forward.
He told the club's website: "We are not obsessed with Llorente. We won't fail to study him because we follow every striker we play against.
"We know their forwards very well, but it is true that Llorente has a specific way of playing that is very effective.
"He personifies the way Athletic play, we know his quality and his strengths and we need to pay very close attention to him."
However, Rodriguez does not believe this weekend will be decisive in the race for fourth place.
"They are three points that will add extra emotion to the game, but I don't think it will completely mark the future," he added.
"I wouldn't give these points more importance than they already have."
Manager Mauricio Pochettino has included new signings Coutinho and Kalu Uche in his squad and both could be involved as Espanyol are still short of attacking options in the absence of Sergio Garcia and Alvaro Vasquez.