The Paris St.-Germain forward needed surgery on a broken metatarsal bone after being injured in a league game on February 25, BBC Sport reported.
Brazil plays its World Cup opening fixture against Switzerland on June 17, a month after his expected return.
"I hope to get there in great shape," said the 26-year-old.
Neymar became the world's most expensive footballer when he joined PSG from Barcelona last August, and has scored 25 goals with 16 assists for the French side this season.
"I get my final examination on May 17 and then I'll be free to play," he told a news conference in Sao Paulo, where he has been receiving treatment.
"I had an examination last week, it is all perfect, evolving well, so I hope that continues so I can get back as soon as possible.
"I am having treatment every day, and from the moment I start training I am going to work harder than I ever worked because this is a dream that's coming up. It's a World Cup. I've waited four years for this chance, it is close."
Neymar played for Brazil, which has won the World Cup five times, at the 2014 finals in his homeland, but missed the 7-1 semifinal defeat by Germany through injury.
Brazil goes to Russia as joint favorites alongside champion Germany. After the opener against Switzerland in Group E, Brazil faces Costa Rica on June 22 and then Serbia five days later.
Neymar, who joined PSG for a fee of €222 million (£200 million), said he was apprehensive about kicking a ball again after almost three months out.
"Of course, doubts exist and I feel them too sometimes," he said.
"But that's normal for a guy who has had the first surgery of his career. It's very difficult for me not playing and not training.
"I have to work even harder but I am going to have enough time to arrive in form for the World Cup, to prepare. It was horrible getting injured but I am more rested, that's the upside. We have to see the positive side of things."