Given that we know very little about gravity and other effects that distort space-time, it's conceivable that faster than light travel may be possible without violating the relativity limit, by distorting space. We don't think that it is possible without producing the ability to travel back in time -- which is considered impossible --, but we also know very little about the subject.

We're nowhere near it, but clearly at the stage of: we know that we know next to nothing about it. Just have a look at the discussion around the Alcubierre Drive and you'll get the feeling that it is pie-in-the-sky science.

So, I'd wager it's not a "very probably no". It's a "we have no clue".