Former Derby County striker Wanchope was rewarded for a successful spell as caretaker coach when the Costa Rican Soccer Federation last month announced that he will stay on in the role.
Costa Rica are unbeaten in six games under Wanchope, who guided his country to victory in last year's Copa Centroamericana.
The Central American nation exceeded expectations to reach the quarter-finals of the World Cup last year, suffering the heartbreak of a penalty shootout exit at the hands of the Netherlands.
Wanchope, who was assistant to Jorge Luis Pinto in Brazil, has now been charged with the task of building on his impressive record so far ahead of the CONCACAF Gold Cup - which starts in July.
The 38-year-old has handed first call-ups to defensive trio Aaron Navarro, Keyner Brown and Lemark Hernandez.
Costa Rica beat Uruguay on penalties in their last friendly back in November after a stoppage-time strike from Johan Venegas had rescued a 3-3 draw in Montevideo to maintain Wanchope's unbeaten record.
Diaz was named Paraguay coach in December and his three-month wait for a first experience of coaching at international level will come to an end on Thursday.
The former River Plate coach took over from Victor Genes, who was put in charge temporarily following Gerardo Pelusso's sacking in June 2013.
Diaz stood down from his role at River after guiding the Argentine Primera Division giants to the title in May and must now look to build some momentum with the Copa America starting in just over two months.
Paraguay begin their Copa America campaign with a daunting clash against Argentina on June 13 and a friendly in Costa Rica should give Diaz a good indication of the size of the task he has taken on.
The Argentine has called up Real Valladolid midfielder Hernan Perez and Cerro Porteno's Fidencio Oviedo to replace Derlis Gonzalez (visa issues) and Nestor Ortigoza (calf), while Raul Bobadilla is set to make his debut.
Paraguay face Mexico at Arrowhead Stadium in Kansas City next Wednesday, while Costa Rica take on Panama a day earlier.
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