"We have known since March that (Antoine) Griezmann is going to Barcelona," Martin said in an interview with Sport, as translated by Get French Football News.
In May, the French superstar informed Atletico of his desire to leave after five seasons.
Although neither club has confirmed the transfer, Griezmann, who is on international duty with France, recently revealed his eagerness to find a resolution.
"I want my future to be decided more than anyone, but there's a need to wait," he said, as translated by Mark Jones of Mirror.
Barcelona will apparently pay the €125-million release clause in the contract extension that Griezmann signed last summer, and the 28-year-old will sign a five-year contract with the Catalan club, according to an earlier report from Sky Sports' Fabrizio Romano.
Although the release clause in Griezmann's Atleti contract is set at €200 million, that figure will drop significantly July 1, according to Isaac Suarez of Marca. Griezmann's former club, Real Sociedad, will reportedly collect roughly €24 million based on the 20 percent sell-on fee agreed in their deal with Atletico Madrid in 2014.
Griezmann evolved into one of the sport's top players following his €30-million transfer from Real Sociedad, scoring 94 goals in 179 league appearances at Atletico Madrid.