In this blog post, Aimee Byrd tells us that she finds David Allen's arguments for Luke being the author of Hebrews to be quite persuasive.
So do I. We don't know for sure, but I think there is a lot going for this suggestion. It is much more likely that it is Luke, than any other New Testament writer.
It is well worth chewing over Allen's book, Lukan Authorship of Hebrews
David Alan Black's The Authorship of Hebrews: the case for Paul is also interesting, but not nearly as convincing.
Hebrews has more in common with Luke and Acts than it does with Paul's letters, I think.