The attacker has described "the happiest day of my life" after Santos accepted bids on Friday, believed to be from Barcelona and Liga rivals Real Madrid
The Brazil international, 21, has been subject to intense interest from Barcelona in recent weeks, and it is widely believed that both the Blaugrana and Real Madrid are behind the offers for the starlet.
And Neymar - who described learning that the bids had been accepted as "the happiest moment of my life" - insists he will take his time over the decision of where he will ply his trade.
"It’s an honour, this is the happiest moment of my life and I am going to give a lot of thought to the two offers," Neymar told reporters in Brazil.
"I’m going to make this decision with my family, there’s no rush. I could make my decision in five minutes, half an hour or three days. My family will help decide what's best for me."
Neymar has long courted interest from a plethora of European giants, with Bayern Munich and Chelsea having both been linked with the player in the past along with the Spanish duo.
The Selecao starlet was named in the longlist for the 2013 Ballon d'Or which was ultimately won by Lionel Messi ahead of his Barca team-mate Andres Iniesta and Madrid forward Cristiano Ronaldo.
Neymar is also part of Luiz Felipe Scolari's squad for the up-coming Confederations Cup, which kicks off in Brazil in June.