Hebrews is formally anonymous. Over the centuries, that has fueled a lot of guesswork regarding the identity of the author. There is, of course, nothing wrong with anonymity. And any ascription of authorship is bound to be conjectural to some degree. But with that in mind, this may be the most interesting suggestion I’ve run across:
“Many biblical figures are named in Hebrews (see chapter 11), but aside from Jesus, the only New Testament person named anywhere in the text is Paul’s associate, Timothy (see 13:23). This seems to eliminate Timothy from consideration as the author, for he would hardly have referred to himself by name. But does it? Some have suggested that 13:22-25 is a kind of brief appendix or postscript to the letter proper, which ends with the long benediction invoking ‘the God of peace–who brought up from the dead our Lord Jesus, the great Shepherd of the sheep’ (13:20). In that case, the ‘voice’ speaking those last four verses may not be that of the author but of someone else forwarding a colleague’s sermon on to its intended audience–or even a different audience, for which it was not at first intended. Possibly the reason this second voice at the end of the letter sounds like Paul (see above) is that it was Paul (so Trobisch 1993:320-323, though without hazarding a guess as to the identity of Paul’s’ colleague). Whoever it was, he mentioned that ‘our brother Timothy has been released from jail’ (13:23). Why is Timothy mentioned? The author of the letter had just asked for prayer ‘that I will be able to come back to you soon’ (13:19), suggesting that he was hindered in some way from coming. The author of the last four verses, by contrast, was not hindered. He was apparently free to come at any time, offering the good news that because Timothy was now free, he and Timothy would come just as soon as Timothy joined him. One possible explanation is that Timothy was the author of the sermon now being sent as a letter ‘to the Hebrews’ (so Legg 1968: 220-23). Timothy, more than anyone else, is named as coauthor (or at least co-sender) of several of Paul’s’ letters (see 2 Cor 1:1; Phil 1:1; Col 1:1; 1 Thes 1:1-2; 2 Thes 1:1; Phlm 1:1), and it is conceivable that here, too, we may have a kind of joint effort. Timothy in prison would have had ample time to compose a long sermon for a specific congregation. This is consistent with the author’s notable interest in ‘those who were thrown into jail’ (10:34), or ‘chained in prisons’ (11:36), or ‘in prison’ (13:3). If this were the case, Paul might then have had the responsibility to see to it that Timothy’s ‘word of exhortation’ reached either its intended audience or perhaps a wider audience than first intended. As he prepared to send it along with his brief cover letter, Paul learned that Timothy had been released and joined with Timothy in his promise to come ‘soon’ in person (13:19,23). Then Paul sent final greetings (13:24) and added to Timothy’s long benediction (13:21-21) a short (and very characteristic) benediction of his own: ‘May God’s grace be with you all’ (13:25). (For further discussion on this see, commentary on 13:22-5).”
“All this is somewhat speculative, yet it offers perhaps the best option for those who feel they must attach a specific name to this memorable ‘Deutero-Pauline’ letter. It was Timothy, after all, whom Paul commanded to ‘focus on reading the Scriptures to the church encouraging the believers, and teaching them’ (1 Tim 4:13). In the book of Hebrews, someone, possibly Timothy, was doing exactly that.”
J. R. Michaels, Hebrews (Tyndale 2009), 310-11.