The 31-year-old, who last week completed a total €5.1m transfer from Barcelona, will reportedly not travel out with the majority of his new teammates on July 25.
Los Colchoneros head out then to South America on a three-stop tour of the continent for preseason friendlies against Estudiantes in Argentina on July 27, Sporting Cristal in Chile on July 31 and Nacional in Uruguay on August 4.
Villa, who began preseason this Tuesday with Atleti at their current base in Segovia, will reportedly be part of the group of players to be left in Spain to continue specific conditioning.
Alongside Diego Godin, Cristian Rodriguez, Oliver Torres, Saul and Javier Manquillo, the striker is seen as standing the best chance of reaching the Supercopa de Espana against his former team Barca in August in the best condition by remaining in Spain.
- Sports & Recreation