The pair start the weekend eight points adrift of seventh-placed Sevilla and behind Valencia on goal difference, but both still have ambitions of forcing their way into the European places.
"Until May 18, until the end of the season, you have to play for every point at stake," said Levante coach Joaquin Caparros.
"There are 30 points left to play for, which means we can still reach the targets we have set. Tomorrow we have three points to work for and we must fight in the match because otherwise we will run out of options."
Levante slipped up last time out, losing 1-0 at home to Celta Vigo, and Caparros has warned his team they are running out of chances.
"We are a team of runs, both positive ones and negatives ones," he said. "Opportunities in football must be exploited and we did not take ours last week."
Espanyol coach Javier Aguirre seemed in more relaxed mood ahead of the match, even with his own future coming under question in recent times.
While he did not address that issue, Aguirre took the time to praise his entire squad on their recent efforts.
"I am satisfied with all of them and I've congratulated them on the work they've done," he said. "Before the Levante game I will pick 11, but it could just as easily be the other 11."
That squad depth could be key in the coming days as Espanyol travel to Malaga in midweek before hosting Barcelona next weekend.
Meanwhile, Levante have announced a new contract with Greek defender Nikos Karampelas until 2016.
"Niko is the type of player who does not complain and sacrifices himself for the club," Caparros said. "He earned this renewal."