Until now, Barça's position was to let him play only the Olympics
One of this season's seruals has been to know which summer is waiting for Neymar. The Brazilian International can play 2 competitions, 2 challenges he said he wanted to play: Copa América Centenario and the Olympic Games of Rio de Janeiro. Copa América will be held from the 3rd to the 26th of june, while the Olympics' football competition will be held from the 4th to the 20th of August.
A priori, the most interesting option for Barça would be that he plays Copa América, a competition that supposedly would only extend the season by 3 weeks, but that would let July and August free for him to go on holiday and to come back later with the team to play, potentially, the Super Cups.
However, Brazil were never crowned in the Olympics, and the fact this year the competition is held at home (Rio de Janeiro) makes it an ideal opportunity for Neymar.
According to what journalist Javi Miguel explained in the Club de la Mitjanit on Catalunya Ràdio on Wednesday, going through the chronology of events, this problem has found itself a solution. Miguel reminded that in the middle of March, just before the International break, Dunga travelled to Barcelona to talk to Luis Enrique and to talk about this summer's schedule.
A few days later, Neymar went with the Brazilian national team and played the first of the two games scheduled with the Canarinha. The player was booked against Uruguay (a fact highly reported in Brazilian press) which prevented him from playing against Paraguay. Miguel explained that the Brazilian player came back before time to Barcelona in a private jet that was already waiting for him in Recife. Therefore, it seems like Neymar had already planned he wouldn't play the second game.
This reinforces Miguel's information: Luis Enrique made a pact with Neymar (with Dunga's approval) that if the forward helps the team to win the Treble, the coach would let him play both competitions: Copa América and Olympic Games.
Here is Miguel's explication in audio, in Catalan: