The Wales international has turned in some brilliant performances in this season's Champions League, including a hat-trick at holders Inter Milan in October.
He has been linked with some of Europe's top clubs, including Real Madrid and Barcelona, but last month signed a new four-and-a-half-year contract with Tottenham through to 2015.
As the Premier League side prepare for Tuesday's Champions League quarter-final first leg at Real, Bale was asked in an interview with Spanish sports daily As whether the new contract was a sign of loyalty to the north London club.
"You never know but I am not scared about leaving the country," he said.
"If a great opportunity comes along then you have to consider it seriously.
"I left home when I was 15. If I leave the Premier League, learn another language and see another country then I will grow as a person."
Asked about Bale at a news conference on Monday, Real coach Jose Mourinho said he would be an expensive purchase and the La Liga club already had similar players such as Cristiano Ronaldo and Marcelo.
"They (Tottenham) like to sell well, very well," the former Chelsea manager said.
"So I think the amount of money involved is not an easy buy. And we have players for that position.
"We have Cristiano, Marcelo. So when you want to spend big money normally you want to do it in areas where you have other problems.
Inter and AC Milan are also big admirers of Bale and have bemoaned not noticing him earlier.
"I think I was one of the first to say he'll be an amazing player and I was saying that when he was not known in Europe, just in England," Mourinho added.
"So I know the great player he is, still young, big space to improve. So he'll be really top top top. No doubt about that."
The winners of the quarter-final will play 2009 champions Barcelona or Shakhtar Donetsk of Ukraine in the semi-finals.
