The men from the Spanish capital made it into the UEFA Champions League quarter-finals for the first time since 1997 with a 5-1 aggregate victory over Milan on Tuesday, sealed by a 4-1 scoreline on the night, but still have a huge part to play in the outcome of the La Liga title.
Simeone's charges currently sit three points adrift of city rivals Real in the Spanish top flight, having leapfrogged third-placed Barcelona - now one point behind Atleti - last weekend.
It is Barca's near-neighbours who visit Vicente Calderon on Saturday, but Atleti will be wary of Espanyol, as the Catalans are one of only three teams to beat them so far this season.
Goalkeeper Thibaut Courtois inadvertently put the ball in his own net on that occasion to see all three points go to the Estadi Cornella El Prat outfit.
Dauntingly for this weekend's visitors, Atleti are yet to lose on home soil in the league this season, scoring 43 goals in just 14 matches, while Espanyol have claimed just three wins on the road.
Diego Costa is second only to Cristiano Ronaldo in the Liga goalscoring charts and found the net once again against in midweek, and Simeone paid tribute to his star striker following that clash.
"He is called to great things and everything that happens to him is thanks to his humility," he said. "No one gave him anything, and everything he´s got is based on his work and passion."
Despite his side putting four past Milan on Tuesday, Simeone is keen to see his players stay grounded and switch their focus back to the league campaign.
"Victories make you strong, as long as you keep your feet on the ground and know what you have to do," he added. "We as a team need to teamwork, not get away from that identity we have had for some time.
"Obviously, the victory itself enhances the team because we will have two more matches of Champions League, and with it, the ability to rotate the players in various positions for all of them to remain at the top."
Javier Manquillo looks set to be the only injury concern for either side, as the Atletico man continues his recovery from a fractured vertebra.
