We say that an object's color is blue if the object is opaque, reflects blue color and absorbs waves of other colors. What color does a transparent object actually reflect?
A truly transparent object doesn't reflect any color in the sense that you seem to mean. How we normally "see" transparent objects is by the refraction of light that they cause and the effect on the image of what lies "behind" them. There is, however, a phenomenon called "total internal reflection" where a transparent object can reflect ALL light that approaches its boundary within a certain range of angles. This is what causes the strange reflection you see when looking up from under water near the surface and how fiber optic systems work.
While I'm very late to the party, the usual definition of "transparent" does allow for the reflection by transparent objects. It is true that "perfectly transparent" material reflects no light at all, but the phrase implicitly allows for materials to be imperfectly transparent.
Generally speaking, objects can be opaque (transmitting no light at all), or they can be transparent or translucent. The difference between transparent and translucent is that a transparent object allows the passage of a reasonably detailed image, while a translucent object does not. And the threshold between the two has no formal definition. A ground-glass is an example of a translucent object - it transmits light with little or no regard for the shape of the source. A car windshield is transparent - you can see through it. Except if the windshield is dirty or scratched, of course, and the worse the dirt or scratches the harder it is to see through, and the closer it comes to being translucent rather than transparent.
As a result, a transparent object can be made which reflects any color you choose. As long as the remaining (transmitted) light can form an image of the source, the object is considered transparent. But not perfectly.