The Brazilian star has been continually linked with a move to both Spanish giants, with Barcelona admitting their interest earlier this week.
However, the 19-year-old has made it clear that he will not be moving any time soon. The forward, seen as one of the world's most promising talents, has admitted that it is his dream to play in Europe one day.
"For now at least I have said no thanks to the interest from Real Madrid and Barcelona," said Neymar.
"I have a contract until 2014 with Santos and I intend to stay and complete it. After that I do not know.
"I dream about playing in Europe, but when that will be I don't know either."
Neymar was recently named the South American Player of the Year.