Ben Olsen's DC are still in pre-season, with their MLS campaign not kicking off until early March.
But they must find some rhythm and form quickly as they prepare for a meeting with Alajuelense at the Estadio Alejandro Morera Soto.
DC attacker Fabian Espindola said his team needed to recover physically as they aim to start the tie well.
"We need to get some good rest and know that we have to go there and do our good job," he told the club's website.
"It's just two games, that's it. The last game is at RFK [Robert F. Kennedy Memorial Stadium] so we need to go and have a good result on the road."
Only one American team has ever made the final of the competition in the Champions League era, which started in 2008-09 - Real Salt Lake in 2010-11.
DC are the only team from the United States left but fellow MLS outfit Montreal Impact are also still alive.
The Impact visit 2009-10 champions Pachuca for their first leg on Tuesday.
Pachuca sit 10th in Liga MX but have won back-to-back games heading into their meeting with the Impact.
America will meet Deportivo Saprissa at the Estadio Ricardo Saprissa Ayma in San Jose.
That tie is between two high-flying teams, with Saprissa leading the way in the Costa Rican Primera Division and America second in Liga MX.
Oribe Peralta, who scored a brace against Chiapas on February 14, and Diego Benedetto (four goals in four games) are sure to play a huge part for America.
There are three Costa Rican teams in the last eight, with the other being Herediano.
Herediano take on Honduran league leaders Olimpia at the Estadio Tiburcio Carias Andino.
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