But Selecao medical staff is set to veto the 22-year-old's attempt at a miraculous return from injury.
The Barcelona forward suffered a fractured vertebra in Brazil's 2-1 victory over Colombia in Fortaleza on Friday.
Brazil's team doctor Jose Luiz Runco said the injury normally required a recovery period of three to six weeks.
However according to Brazilian newspaper Folha de S. Paulo Neymar has expressed a wish to return for the tournament decider on July 13 in the event Brazil advances.
"Neymar says that he is feeling less pain and for that reason he thinks he can recuperate in one week," the newspaper said.
"Medical staff concedes the injury isn't so serious but say there is no way the fracture can heal in that period."
Neymar has left Brazil's training base in Teresopolis, north of Rio de Janeiro, to recover with his family in the Brazilian port city of Santos.