According to the FIDE rules, it is not forbidden; clock times are actually explicitly stated as one of the items that a scoresheet may contain. See the following excerpt (emphasis mine):
Article 8: The recording of the moves
a. In the course of play each player is required to record his own moves and those of his opponentin the correct manner, move after move, as clearly and legibly as possible, in the algebraic notation (Appendix C), on the ‘scoresheet’ prescribed for the competition. It is forbidden to write the moves in advance, unless the player is claiming a draw according to Article 9.2, or 9.3 or adjourning a game according to Appendix E.1 a.
b. The scoresheet shall be used only for recording the moves, the times of the clocks, offers of a draw, matters relating to a claim and other relevant data.
c. A player may reply to his opponent’s move before recording it, if he so wishes. He must record his previous move before making another.
d. Both players must record the offer of a draw on the scoresheet with a symbol (=).
e. If a player is unable to keep score, an assistant, who must be acceptable to the arbiter, may be provided by the player to write the moves. His clock shall be adjusted by the arbiter in an equitable way. This adjustment of the clock shall not apply to a player with a disability.
Note that the rules above pertain to competitions starting on or after July 1st, 2014. The older version has the same rule placed in article 12.4. (thanks to @chaosflaws)