Yes, it doesn't, but that's your answer because there is no single, exclusive English word for sexually desiring someone. So there can't really be one that exclusively refers to sexually fantasizing about them, at least, not until the age of extensive psychological and sociological taxonomies.

My response to your finding it difficult to believe is: you're asking for a word for an intensely private act! Think about how rarely people overtly and bluntly say they are sexually fantasizing about someone. When it's actually admitted to, it's done using a variety of metaphors, slang and indirect hints.

And in general, we don't have a commonly used prefix or second compounded word to turn a physical act into a fantasy. Even though "fuck" predates Early Modern there was nothing commonly attached to it to make it mental.