Yes, books could serve as currency, because currency can be any type of medium. A large book could be worth more than a small book. Two books could be worth more than one. If books were scarce, this would be a way to allocate goods. This would work much like money.
Books could be used as currency. Rare books contain valuable information unavailable to everyone. This would open up the use of rare books collecting dust in a vault that aren't able to be read by everyone. It would also allow the government to purchase books and better educate the public.
Books would not make a good form of currency for a variety of reasons. First, unlike cash or credit cards, they would generally not be easy to carry. If books are not assigned a high monetary value, there would be no incentive to carry them. Further, if they WERE assigned a high monetary value, given that you can easily see a person carrying a book, I feel that people would be robbed frequently. Next, how would you even begin to assign value to a book? Is it based solely on page count? Is it based on the quality of the book? Who would determine what's a quality book? Is it based on the age of the book, the edition of the book? There are too many variables to allow for books use of currency.
I do not think books could serve as currency. Whatever medium serves as currency has to have a set value so that everyone knows how much purchasing power they have. Books are creative endeavors, with multiple genres. The value of a certain book fluctuates as it's popularity rises then falls. We would need a medium with more stability than books.