Suarez's return from a four-month suspension for biting Giorgio Chiellini has not gone to plan, with Barca beaten by Real Madrid and Celta Vigo in his first two competitive appearances for the club.
The Uruguay striker will be eager to end that run when he makes his Champions League debut for the Catalan giants against the club where he shot to prominence.
Suarez scored 111 goals in 159 games in a three-year spell with Eredivisie champions Ajax before moving to Liverpool, and Barca will be eager to see him rise to the occasion in Amsterdam.
The Catalian giants have slipped to fourth in La Liga after suffering a 1-0 home loss against Celta on Saturday, a week after their 3-1 El Clasico defeat at the Santiago Bernabeu.
Coach Luis Enrique urged the Catalan giants to "stand up" and "move forward" following their defeat at Camp Nou at the weekend.
A victory in Amsterdam will see Barca progress from Group F if APOEL fail to beat Paris-Saint Germain and Spain midfielder Sergio Busquets is determined to respond from their recent setbacks.
"We've had a bad week," he said on Monday. "What we want to do now is turn things around.
"Hopefully we can put an end to this poor run."
Ajax secured a 2-1 home win over Barca in last season's group stages despite playing much of the second half with 10 men following Joel Veltman's sending off, which resulted in Xavi putting the visitors in front from the penalty spot.
And Busquets is wary of the threat posed by Frank de Boer's side.
"They came out strong and were all over us at the start of the game." he said. "With the sending off and our goal, everything changed. I hope it doesn't happen again."
Lionel Messi has not scored in Barca's last two games and he needs another two strikes to equal Raul's record of 71 Champions League goals, with Cristiano Ronaldo just one shy of the mark set by the Real Madrid legend.
Andres Iniesta and Jeremy Mathieu miss out due to calf injuries, while Sergi Roberto (groin) and Thomas Vermaelen (thigh) are also sidelined.
Ajax will move just a point behind Luis Enrique's men if they are secure three precious points on Wednesday.
De Boer's team warmed up for the crunch clash by hammering Dordrecht 4-0 on Saturday and they have reeled off three wins in a row, scoring 11 goals in the process.
The Dutch club - who lost 3-1 at Camp Nou a fortnight ago - will be without forward Viktor Fischer due to a hamstring problem.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.