The Brazilian national team doctor has flown to Paris to assess Neymar's injury, but Paris Saint-Germain will have the final say on how to treat the fractured foot and ankle sprain.
PSG coach Unai Emery denied reports Neymar will require surgery, saying the Brazil forward needs rest and could still recover in time to face Real Madrid in the Champions League next week.
"Neymar is not going to be operated on, this information is false," Emery said.
However, the player's father, Neymar Santos, said he thinks his son does need surgery and expects him to be sidelined for up to eight weeks -- ruling out any chance of him playing against Madrid.
"We have to think about him as an athlete. PSG knows they won't have Neymar at the very least for six weeks. The treatment will last between six and eight weeks regardless of a surgery," Neymar Santos told ESPN Brasil.
The Brazilian soccer federation's technical coordinator Edu Gaspar said it would "respect" the view of the PSG medical staff, despite the national team doctor flying to Paris.
"Neymar is under the care of Paris Saint-Germain," Edu said after a World Cup meeting in the Russian resort of Sochi. "Until Paris Saint-Germain decides on his future in terms of training or so on we will continue to wait. A doctor from Brazil has gone to accompany him and monitor the news from Paris Saint-Germain."
The injury comes with less than four months until Brazil opens its World Cup campaign against Switzerland on June 17.
"We cannot think about the World Cup yet," Edu said.
PSG broke soccer's transfer record last year by paying Barcelona 222 million euros ($260 million) to buy Neymar.
Neymar was hurt on Sunday as the French league leader beat Marseille 3-0. After tests revealed he has a cracked fifth metatarsal in his right foot along with an ankle injury, reports suggested Neymar opted for surgery and he would be sidelined for up to two months.
Metatarsal injuries are common in soccer and can sometimes lead to a lengthy absence from the pitch. After speaking with the club doctor, Emery said Neymar has a "small crack in the fifth metatarsal."
"We'll see how things evolve in the coming days before making a decision with him," he said.
Emery did not say how long Neymar will be sidelined but insisted "there is a small option he can be ready for the match" against Madrid. PSG trails 3-1 from the first leg of the last-16 matchup in the premier European competition that Neymar was signed to win for the French capital club.
Emery said he did not feel he made a mistake by letting Neymar play against Marseille despite the crucial Champions League match looming.
"We normally try to protect him by planning things ahead with him, but it was normal to have him play against Marseille, it was an important game," Emery said.
Asked if PSG was pressured by Brazil in its dealing with Neymar's injury, Emery said his team remains his priority.
"The most important thing is us, although the World Cup matters to every player," Emery said. "Neymar wants to play against Real Madrid and we are focusing on this."
Despite spending lavishly since they took over PSG in the summer of 2011, the club's Qatari owners have so far failed in their bid to establish the club as a European force. PSG has been dominating the French league but has failed to get past the Champions League quarterfinals, losing in the round of 16 last year following a 6-1 humiliation at the hands of Barcelona in the second leg.