AMSTERDAM (Reuters) - The U.S. dollar's value is dropping so fast against the euro that small currency outlets in Amsterdam are turning away tourists seeking to sell their dollars for local money while on vacation in the Netherlands.

"Our dollar is worth maybe zero over here," said Mary Kelly, an American tourist from Indianapolis, Indiana, in front of the Anne Frank house. "It's hard to find a place to exchange. We have to go downtown, to the central station or post office."

That's because the smaller currency exchanges -- despite buy/sell spreads that make it easier for them to make money by exchanging small amounts of currency -- don't want to be caught holding dollars that could be worth less by the time they can sell them.

The dollar hovered near record lows on Monday, with one euro worth around $1.58 versus $1.47 a month ago.

(Reporting by Svebor Kranjc, writing by Reed Stevenson)