The book of Hebrews and Clement of Rome?

In my recent study of the First Epistle to the Corinthians by Clement of Rome for my Christian and Jewish literature blog (which has still yet to get off the ground really), I began to notice some similarities between the styles of the author of Hebrews and Clement's letter. Maybe they are juss coinicidences, perhaps a result of sharing similar backgrounds (the author of Hebrews seems to have been from Italy, like Clement, as Hebrews 13:24 indicates), or a variety of other possible explanations.

I have yet to really focus in on the idea though, so I haven't fully collected my thoughts on it. However in brief research online that I have done, it apparently has been suggested in the past that Clement authored Hebrews.

Here are a few things I noticed: Both letters have a heavy reliance upon the Old Testament. Additionally, the quotations can be quite lengthy in both. Third, both are from Italy. Also, both authors are fond of using Old Testament people as examples for behavior (see Hebrews 11). Finally, the tone of the two letters seem similar. Now, I haven't compared the two letters in greater detail, but it is something I am probably going to pursue.

Now certainly, there are some difficulties with Clement being the author. For instance, Hebrews 2:16 seems to suggest the author himself was an Israelite. In order for Clement to be the author, either we have to go against the generally accepted idea that Clement was a Gentile (though by no means proven) and declare him to be a Jew or we have to see the references to the descendants of Abraham not in the literal sense of physical descendants, but rather in metaphorical sense to include all people who mimick Abraham in his faith (like Paul in Romans 4:16 and Galatians 3:29).

The latter is possible, since Clement may have been a disciple of Paul (if he is indeed the Clement of Philippians 4:3) and the author of Hebrews seems to have a disciple of the apostles (Hebrews 2:3-4). However, past conjecture, we have little exegetical means to ascertain that the author was speaking metaphorically in Hebrews 2:16 instead of literally. Secondly, if it is metaphorical, then we will have to probably change the idea that the audience is Jewish. That is problematic with the amount of quotations from the Old Testament and the detailed exposition of it, indicating a good knowledge of the Old Testament by the audience. However, then again the letter to the Corinthians by Clement does contain plenty of Old Testament quotations.

This is just a brief look at the question of the authorship of Hebrews. I will perhaps, with some more in depth comparison of the two letters, write a longer post on the topic. However, I am curious as to what you all think about this possibility of Clement authoring Hebrews. Any other similarities that could support it that I haven't gotten to you, or problems that could lead one to deny the idea?