The Brazil international, who helped Diego Simeone's men to Copa del Rey glory last season, feels los Colchoneros are just a few players short of challenging for the Liga title
Los Colchoneros ended last season on a high, beating los Blancos at the Santiago Bernabeu to win the Copa del Rey, but only after their championship challenge had faded away, with Diego Simeone's men ultimately finishing a distant third in the table.
However, Miranda has been buoyed by Villa's arrival from Camp Nou, and feels that with a few more shrewd additions, Atleti can challenge the Clasico duo for the top prize in Spain.
“With David Villa and a couple more signings, yes, I think we can compete with Barca and Madrid,” the defender told AS.
“Because they have great squads, we also need a quality team in order to fight them on equal terms.
"Our goal is to fight for the title in every competition that we compete in and the first objective is to win the Supercopa against Barcelona in August."
Villa's arrival in Madrid swiftly followed Neymar's move to Barcelona and Miranda is backing his fellow Brazilian to achieve great things in Catalunya.
"He is a great player and he will certainly succeed at Barca," the 28-year-old enthused.
"I wish him well in the Spanish League. I will follow him and support him, less so when he plays against Atletico!"
Miranda joined Atletico Madrid on a free transfer from Sao Paulo two years ago.