With just one win in their last four Liga matches, champions Atletico have slipped to seven points behind leaders Barcelona.
Griezmann was suspended for Sunday's 1-1 home draw with the fourth-placed Valencia.
But returning to the frame for Saturday's road trip, Griezmann wants his team-mates to get back to enjoying themselves.
"After not being able to play last week due to suspension, I'm eager and excited to try help the team," Griezmann told Atletico's official website.
"The keys to the match against Espanyol will be, be strong at the back and at the front.
"And when we have the ball, try to combine to have fun, because in the end, [it] is a game and when we enjoy ourselves, we play very well."
Griezmann, speaking after winning Atletico's Liga player of the month for February, has already netted 14 goals in the league this season.
He is determined to beat his best of 16, achieved last year with Real Sociedad, and added: "I hope to improve my performance even more but I'm having fun on the field and you can see that.
"When I arrived here, I said that I wanted to improve my goal number and I'm working on it.
"I'm giving my best and I hope to exceed the 16 goals I scored last season."
That news is ominous for Espanyol, who have the worst defensive record of any team in the top half of the table.
The 10th-placed side have lost their last two and need forwards Sergio Garcia and Cristhian Stuani to rediscover their form.
The pair, who have scored nine Liga goals this season each, but have between them contributed just one goal in Espanyol's last five games.
Espanyol will hope that Atletico are distracted by their upcoming UEFA Champions League clash, though.
Diego Simeone's men trail Bayer Leverkusen 1-0 after the first leg of their last-16 clash. Atleti will host the return match on Tuesday.
Atletico have won five of their last six clashes against Espanyol. Four of those five victories have come with a clean sheet.
Tiago and Mario Suarez scored in the 2-0 success they posted in October but Espanyol will take solace from their triumph when Atletico last visited them, sealed by a Thibaut Courtois own goal.
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