As -zag points out below, lay-offs are a useful way to rid the company of the lowest performers, so management prefers to make the decisions. Whether or not you’ll be able to volunteer depends on at least a couple of factors.
If you’re area of expertise and assignment(s) are in productive, profit producing mainstream projects and you’re a key player/high performer (based on merit reviews, not your own, possibly distorted view of yourself) then you’re less likely to have management accept you as a volunteer. If you have a good personal relationship with your supervisor, including up to director level where the real decision power starts, then you’re more likely to be accepted.
Now I’ll mention a very important factor to consider when deciding whether or not to volunteer- If you’re not accepted, you may be damaging your future career advancement possibilities and review ratings. You might be considered a “short-timer” who’s loyalty is in question and have management favor others over you for both promo and the limited number of very high review ratings that can be given out.
Two last points-
If you’re considering this, time is extremely short. You may have missed the opportunity already. Management is well underway on creating the lists.
It generally isn’t the managers who are creating the lists. Though some of them may have influence, it’s really at the director level and above where the decisions are made, so don’t just volunteer to your manager (unless he/she is director or higher). In fact, you may want to speak with your director about this and NOT say anything to anyone else, including your manager. In the event that you’re not accepted, you could hope that your manager never knows you volunteered (doubtful) in an attempt to do minimal career damage.
I would say you basically have to be ready to walk if you’re considering volunteering. Maybe tell management that regardless of the answer, you will be leaving the company.