Brazil coach Dunga has suggested that Kaka was unable to make his national team cut for Copa America because his training with Major League Soccer side Orlando City was not rigorous enough.
The 34-year-old Orlando City star had replaced injured Bayern Munich winger Douglas Costa in the team two weeks ago, but was himself ruled out of the competition just five days later with an injury.
Brazil, who routed Haiti, 7-1, on Wednesday, have had to replace a total of six players on the Copa roster, including Rafinha, Ederson, Ricardo Oliveira and Luiz Gustavo.
"Kaka is one of the reference points or trademarks of Brazilian football," Dunga told the Orlando Sentinel. "He's been unfit the last two appearances, he had an injury. Maybe it is because of the training of the Brazil team, the quality and intensity of the game maybe is different from what he's used to.
"But, football is something you can never be definite about. You never know what tomorrow will bring. You can never say never."
Kaka, who played in a friendly against Panama last month, has been capped 92 times for Brazil, scoring 29 goals.
Orlando City's vice president of communications, Diogo Kotscho, took issue with Dunga's comments about the club's training methods. He said Kaka had twice joined the Selecao and was returned injured to the club.
"It is very sad to see someone using prejudice to justify Kaka's injury," Kotscho told the newspaper. "MLS is a very physical league and the work we do here and all over MLS with the players is referenced worldwide. Our training facility and professionals are world class.
"Brazil has five injured players in one week, players from many places. MLS has some weaknesses; Physical training for sure isn't in this list. He can't come to our city [and] disrespect professionals that he doesn't know without answer."
It is uncertain if he will be ready in time to play when the Lions return to MLS action and host the San Jose Earthquakes on June 18.