The Selecao will be in USA from June 3-26 for an extended version of the Copa America to mark the tournament’s centenary, before competing at the Rio Olympics between August 4-26.
Coach Dunga will lead his side in both tournaments but may have to do without his captain for one of them.
“At first, yes [the idea was to use him in both competitions], but let's talk to the players and the clubs,” Gilmar told Globo.
“In the coming days Dunga will give me names of the three over-age players he proposes for the Olympics.
“After the qualifiers in March, against Uruguay and Paraguay, we will talk personally with those players.”
Football clubs are under no obligation to release players for the Olympic Games and Barcelona are keen not to risk Neymar burning out prior to the start of the European season.
Argentina coach Gerardo Martino said this week his Olympic squad will not include Lionel Messi, who was previously granted leave by Barcelona for the 2008 games in Beijing.
Neymar has repeatedly expressed his desire to compete in both competitions but is believed to be prioritising the Olympic games in a bid to lead the five-time world champions to the only remaining major title they are yet to win.
“The player really wants to play the Olympics, which take place when he’s on holiday [at the end of the season],” added Gilmar.
A tournament for players under-23, each team is allowed to select three over-age players.
Neymar competed for Brazil in the 2012 London games which saw his side lose the gold medal match to Mexico.