The World Cup, where Brazil are aiming for a sixth title, starts in Russia on June 14.
The 35-year-old picked up a knee ligament injury during his side's 2-0 triumph over Les Herbiers on Tuesday, May 8 in the French Cup final.
"As it has been since the beginning of the work, the technical committee has created an important relationship with the teams from Brazil and abroad, which allows for technical, physical and clinical follow-ups [.] as well as participation in decision-making".
The front-runners to be his replacement were Manchester City's Danilo, Corinthians' Fagner, and Bayern Munich's Rafinha.
BC-SOC-Brazil-Alves, 1st Ld-Writethru, 258 Brazil right back Alves out of World Cup after knee injuryAP Photo REB185Eds: Adds quotes, context, bylineBrazil right back Dani Alves will miss the World Cup.
Meanwhile, reports coming from the south American country claim the defender will not be able to travel to Russia at all. "He wants to recover as fast as possible".
Gaspar also said Brazil coach Tite has enough information to pick an adequate substitute at right back.
Cafu is the player with the most appearances for Brazil with 142 matches, followed by former Real Madrid star, Roberto Carlos - 125.
Tite is due to name his squad on Monday.
Brazil's first game in Russia will be on June 17 against Switzerland.