It is perhaps not a bad idea to be aware of the controversy currently surrounding the word "müsait": http://www.todayszaman.com/national_turkish-language-body-to-review-definition-of-available-due-to-claims-of-sexism_374961.html
The controversy isn't over the word so much as the way in which the TDK writes its dictionary definition. There is a slang meaning of the word that means, unsurprisingly, sexually available or easy, and the TDK's definition specifies that it's a descriptor of women. Essentially it's more of a debate over whether a dictionary's definitions can truly be "objective" and separate from the actual cultural dialogue of word usage, not so much over the actual usage of one word.
Mostly just wanted to clarify that second language learners don't need to worry about the slang meaning (though the debate itself is interesting!). It's perfectly acceptable to say "müsaitim" to indicate that you're available to talk or whatnot, and no one would interpret an off-color meaning, regardless of your gender. I have a very hard time imaging any way a TSL learner would accidentally misuse the word in a slang sense.