Paraguay, who have reached the last four World Cup tournaments, will not be able to reach next year's event in Brazil unless they beat the group leaders in Asuncion.
The qualifying campaign has been poor from start to finish from Paraguay, who have not recovered from losing six of their first eight matches.
They have failed to replace manager Gerardo Martino, who declined to renew his contract in 2011 following the Copa America tournament.
Martino, who took Paraguay to the quarter-finals of the 2010 World Cup, is now in charge at Barcelona.
Both Francisco Arce and Gerardo Pelusso have lost their jobs in charge of the nation during qualifying, with Victor Genes the current coach.
Genes saw his side move off the bottom of the South American qualification group with a convincing 4-0 win over Bolivia on Friday.
Jonathan Fabbro, Roque Santa Cruz, Richard Ortiz and Gustavo Gomez all scored in that match, but the result came far too late for Paraguay.
They have just 11 points from 13 qualifying matches and are sure to be tested by Argentina.
With Brazil not involved in the group – they reach the tournament automatically due to being the host nation – Argentina have enjoyed a productive qualification campaign, losing just one of a possible 13 fixtures.
Of those matches, seven have been wins, with Real Madrid's Gonzalo Higuain (nine goals) and Barcelona star Lionel Messi (eight goals) in excellent form.
Higuain is suspended for this encounter, as are Javier Mascherano, Federico Fernandez and Diego Garay.
But manager Alejandro Sabella has no shortage of options to choose from to replace Higuain, with Manchester City's Sergio Aguero, in-form Inter striker Rodrigo Palacio and PSG's Ezequiel Lavezzi in the squad.
Argentina have not played a competitive match in almost three months, though, with 4-0 and 2-1 friendly wins over Guatemala and Italy filling their schedules in the meantime.
They were victorious the last time the sides met, with goals from Angel di Maria, Higuain and Messi giving them a 3-1 home win in September last year.
And a similar result seems likely on Tuesday, with Paraguay's miserable qualifying campaign set to be finally ended.
