Their requests, if granted, will put a damper to Coach Dunga's plans to field a full-strength squad for the South American championship.
In a letter to Brazil's technical staff, Ronaldinho said he needed to rest after his season with Barcelona ends in June 17.
"It is well known to you that during the last few years I have been subjected to intense and uninterrupted physical activity," he said. "I have been unable to take the recommended and necessary periods of rest which may, on occasion, have an influence on the high level of performance demanded by my professional commitments with my club and, principally, the Brazilian national team. I have always shown satisfaction and a sense of responsibility in serving Brazil during my career. Wearing the yellow shirt is, for me, a motive of pride and love for my country."
In Kaka's letter, published on the Web site of his Italian club, AC Milan, the Brazilian star said he had not rested for three seasons and therefore requested to be left out of the Copa America.
Kaka is the leading scorer in the 2006-07 UEFA Champions League. His inspirational play has led Milan to the final on May 23 in Athens against Liverpool.
Ronaldinho has been having what would for him be described as a "down year" for Barcelona in Spain's La Liga, but he has still scored 18 league goals.The last day of La Liga season is not scheduled until June 17, nine days before the start of the Copa America.
There is a precedent for the wishes of Ronaldinho and Kaka to skip the Copa America to be granted. Stars Ronaldinho, Ronaldo and Roberto Carlos missed the 2004 Copa America in Lima, where Brazil still won with a "B" team.
Brazil fans should get some idea of Dunga's intentions for the summer he announces on Thursday the squad he will take for friendly games against England on June 1 at Wembley Stadium and Turkey four days later in Dortmund, Germany.