Four-times European champions Ajax travel to Spartak Moscow for a last-16 return match 1-0 down from last week's first leg while Liverpool face Portuguese upstarts Braga at Anfield trailing by the same score.
Suarez scored 81 league goals in less than four seasons with Ajax before leaving for Liverpool in January and the Dutch team could certainly have done with his nose for goal in Russia, having dominated the game and missed a hatful of chances.
Liverpool will also be unable to count on the 23-year-old forward because he is cup-tied.
"We would much rather have Luis playing in the Europa League but then we would much rather have him for a long-term contract than just for three months," manager Kenny Dalglish told Sky's website.
"We are happy he is at the club and we just need to wait."
Although Suarez is absent, plenty of other South Americans have been enjoying themselves in Europe's much-maligned second-string tournament.
South American players grabbed winners in four of last week's eight ties and Colombian Radamel Falcao Garcia tops the overall scoring charts with seven goals for Porto.
Brazilian midfielder Alex Meschini poached Spartak's winner at Ajax and compatriot Nilmar netted twice to give Villarreal a 3-2 win at Bayer Leverkusen and put his side in the driving seat in the clash between the only surviving Spanish and German teams.
Portuguese sides Porto and Benfica regularly feature up to eight South Americans in their starting line-ups, with Colombians and Argentines joining the more familiar Brazilians.
Porto have been a dominant force in the competition this year, losing only one out of 11 games, and are strongly placed to progress as they host CSKA Moscow with a 1-0 lead from the first leg in Russia.
SUPERB STRIKE
The winner was courtesy of a superb strike from Falcao's fellow Colombian Fredy Guarin.
Benfica's line-up could include Paraguay World Cup striker Oscar Cardozo, experienced Argentines Pablo Aimar and Javier Saviola and bright prospects for the future in Franco Jara and Eduardo Salvio.
Salvio is hoping to collect a winner's medal for the second year running, having been part of the Atletico Madrid squad that lifted the trophy last year.
"I had a wonderful experience in the Europa League with Atletico. Now I am feeling the same with Benfica," said the 20-year-old whose team take a 2-1 lead to Paris Saint-Germain after goals from Uruguayan Maxi Pereira and Franco Jara.
"I think we can score in France... we all know it will be a very difficult game but we have very good, experienced players who can help us through."
Liverpool's Brazilian midfielder Lucas is another Europa League fan.
"For me it's a big competition," he said. "Maybe some people don't give this competition too much importance but in Brazil the Eur
