Copa Libertadores: Six group spots up for grabs
The first stage sees six two-legged play-offs take place, with the winners advancing and the losers' campaigns over by mid-February.
Nacional are three-time champions, but the last of those titles came in 1988.
The Uruguayans will face Palestino, with the first leg to be played in Chile on Thursday.
While Palestino have made a solid start to their Chilean Primera Division campaign, Nacional may be lacking match fitness.
Alvaro Gutierrez's men, comfortable Apertura champions in Uruguay, are yet to start their Clausura campaign.
Nacional beat Penarol 1-0 in a friendly in mid-January, and Gutierrez will be confident his team are in a good enough condition to get something from their trip to Chile.
Veteran striker Ivan Alonso is the man to watch.
The 35-year-old former Espanyol man scored 15 Apertura goals and is a regular threat.
Argentine outfit Estudiantes, who are four-time Libertadores winners, are also in action on Thursday.
Mauricio Pellegrino's men travel to Ecuador to take on Independiente del Valle in their first leg.
Elsewhere, Argentine club Huracan visit Peru to take on Alianza Lima on Tuesday.
Liga MX side Morelia host Bolivia's The Strongest, while 2012 champions Corinthians take on Once Caldas.
Venezuelan outfit Deportivo Tachira will welcome Cerro Porteno to the Estadio Polideportivo de Pueblo Nuevo on Wednesday.