The young Argentine forward failed to establish himself as a starter at Calderon last season and the capital club have decided to cash in on him.
Vietto made 28 appearances for Atletico Madrid last season, scoring just three times.
Atletico Madrid are looking to sign the Sevilla striker Kevin Gameiro apparently.
Mundo Deportivo are claiming that Barcelona backed out of a deal to sign the French striker because of his age and price and have agreed a deal for Vietto instead.
The Spanish newspaper claims that the fee will be 22 million Euros and the Argentine should join Luis Enrique’s side soon.