John Calvin Commentary Hebrews 13:23

"Know ye that our brother Timothy hath been set at liberty; with whom, if he come shortly, I will see you." — Hebrews 13:23 (ASV)

Know ye that our brother, etc. Since the termination of the Greek verb γινώσκετε will admit of either rendering, we may read, “You know,” or, “Know;” but I prefer the latter reading, though I do not reject the other. The probability is that he was informing the Jews on the other side of the sea of what they did not know.

Now, if this Timothy was the renowned companion of Paul, which I am inclined to think, it is very probable that either Luke or Clement was the author of this Epistle.

Paul, indeed, more usually calls him his son. Consequently, what immediately follows does not apply to Paul, for it appears that the writer was at liberty and at his own disposal. Furthermore, he was then anywhere rather than at Rome. In fact, it is very probable that he was then going around through various cities and was then preparing to pass over the sea. Now all these particulars might have been suitable to the circumstances of either Luke or Clement after the death of Paul.