Technically it would translate to "I'm not sleepy" as Alexander stated. However, I would like to point out that, at least in my my area, we don't typically say that. Instead, it is much more common to say "I'm not tired" (technically «no estoy cansado») with the same meaning.

"No tengo sueño" means "I'm not sleepy". "No tengo sueños" means "I don't have dreams"