I don't think it's something that can be definitively answered. We are never told that Legolas had any brothers or sisters, but simply because we aren't told doesn't mean it can't be inferred.
Not much is known on Legolas, probably because of the late development of the character (Legolas wasn't even a character thought about by Tolkien when he was writing The Hobbit). But, I've always found interesting why would Thranduil send his only son and heir as a messenger? Because that's what Legolas was at the Council, he was delivering a message. Now why would Thranduil send his only son away (when they are facing attacks from Dol Guldur) as a messenger?
I'm not saying that for sure Legolas had siblings, but I don't think it's something that can be answered with a simple, 'No it's not possible.'
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Fenris Penguin
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