My real position is that no one but God knows who wrote it. (I started to go back and correct myself to credit Origen for saying that; but then I realized that in this post-Driscoll/Taylor/Tyndale day, that sort of thing is passé.)
But, if the writer is anyone we meet and know anything about in Scripture, it's likeliest to be Apollos. Alford (see, just can't break the habit) said it about as well as can be done, so here it is from his commentary's introduction:
180. There is yet one name remaining, that of APOLLOS, in whom certainly more conditions meet than in any other man, both negative and positive, of the possible authorship of our Epistle. The language in which he is introduced in the Acts (18:24) is very remarkable. He is there described as Ἰουδαῖός τις, Ἀλεξανδρεὺς τῷ γένει, ἀνὴρ λόγιος, δυνατὸς ὢν ἐν ταῖς γραφαῖς. Every word here seems fitted to point him out as the person of whom we are in search. He is a Jew, born in Alexandria: here we have at once two great postulates fulfilled: here we at once might account for the Alexandrian language of the Epistle, and for the uniform use of the LXX version, mainly (if this be so) in its Alexandrian form. He is an eloquent man (see note on λόγιος ad loc., Vol. II.), and mighty in the Scriptures. As we advance in the description, even minute coincidences seem to confirm our view that we are here at last on the right track. He is described as ἐπιστάμενος μόνον τὸ βάπτισμα τοῦ Ἰωάννου, but being more perfectly taught the way of the Lord by Aquila and Priscilla. No wonder then that a person so instituted should specify βαπτισμῶν διδαχή as one of the components in the θεμέλιον of the Christian life (Heb. 6:2). It is described as his characteristic, that he ἤρξατο παῤῥησιάζεσθαι ἐν τῇ συναγωγῇ: is it wonderful then that he, of all N. T. writers, should exhort μὴ ἀποβάλητε τὴν παῤῥησίαν (Heb. 10:35), and declare to his readers that they were the house of Christ ἐὰν τὴν παῤῥησίαν … κατασχῶμεν (Heb. 3:6)?
181. Nor, if we proceed to examine the further notices of him, does this first impression become weakened. In 1 Cor. 1–4, we find him described by inference as most active and able, and only second to St. Paul himself in the church at Corinth. It would be difficult to select words which should more happily and exactly hit the relation of the Epistle to the Hebrews to the writings of St. Paul, than those of 1 Cor. 3:6, ἐγὼ ἐφύτευσα, Ἀπολλὼς ἐπότισεν. And the eloquence and rhetorical richness of the style of Apollos seems to have been exactly that, wherein his teaching differed from that of the Apostle. It is impossible to help feeling that the frequent renunciations, on St. Paul’s part, of words of excellency or human wisdom, have reference, partly, it may be, to some exaggeration of Apollos’ manner of teaching by his disciples, but also to some infirmity, in this direction, of that teacher himself. Cf. especially 2 Cor. 11:3.
182. It is just this difference in style and rhetorical character, which, in this case elevated and chastened by the informing and pervading Spirit, distinguishes the present Epistle to the Hebrews from those of the great Apostle himself. And, just as it was not easy to imagine either St. Luke, or Clement, or Barnabas, to have written such an Epistle, so now we feel, from all the characteristics given us of Apollos in the sacred narrative, that if he wrote at all, it would be an Epistle precisely of this kind, both in contents, and in style.
183. For as to the former of these, the contents and argument of the Epistle, we have a weighty indication furnished by the passage in the Acts: εὐτόνως γὰρ τοῖς Ἰουδαίοις διακατηλέγχετο δημοσίᾳ, ἐπιδεικνὺς διὰ τῶν γραφῶν εἶναι τὸν χριστὸν Ἰησοῦν. What words could more accurately describe, if not the very teaching itself, yet the opening of a course of argument likely, when the occasion offered, to lead to the teaching, of our Epistle?
[Alford, H. (2010). Alford’s Greek Testament: an exegetical and critical commentary (Vol. 4, pp. lviii–lix). Bellingham, WA: Logos Bible Software.]
I bolded the sentence that best sums it up. You could just lift the description of Apollos in Acts, and append it to Hebrews as the "author blurb."