The 20-year-old is one of world football's most sought-after young talents, with his performances in his homeland attracting the attention of some of the game's biggest clubs.
Barcelona were widely believed to be the frontrunners to sign the striker, though Real Madrid, Chelsea, Manchester City and Manchester United have all been credited with an interest.
Santos president Luis Alvaro de Oliveira Ribeiro revealed earlier this month that a proposed move to Stamford Bridge over the summer never materialised, while Man City boss Roberto Mancini has said he would discuss Neymar's situation with new director of football Txiki Begiristain.
Neymar himself has always been keen to play down any talk of a move to Europe, stressing the benefits of developing his game in the Brasileirao.
That has not stopped the speculation, however, and the forward appeared exasperated when he was quizzed about his future in New Jersey, where he is with the Brazilian national team for a friendly with Colombia.
"When will you stop asking me that? I'm tired already," he told Globo Esporte.
"I have a contract with Santos until 2014 and I intend to see it out.
"If I stay or leave before that it's up to Santos' president."
Former Brazil striker Ronaldo believes Neymar faces a difficult balancing act between his own development as a player and his status as the poster-boy for Brazilian football.
"This is a complicated matter because it involves Brazilian passion, our biggest idol at the moment and our will to see him playing here every weekend," the 36-year-old told Arena Sportv.
"But for his career development, to fight to be the world's best player, he should be playing for a big European club.
"If would be interesting for the national team if he played for a big European club, so that he would be ready and experienced to face any defence in the World Cup.
"If he goes to Europe, he'll be fighting for the world's best player award with Crisitano Ronaldo and [Lionel] Messi."