No, only those in the reaping can volunteer.
Victors who are still of reaping age would not be allowed to volunteer to take someone’s place in the Hunger Games. The rule of volunteering for the Hunger Games is that another eligible candidate - meaning someone whose name would have been put into the reaping balls but not chosen - can take the place of the one who was chosen.
“The rule is that once a tribute’s name has been pulled from the ball, another eligible boy, if a boy’s name has been read, or girl, if a girl’s name has been read, can step forward to take his or her place.”
- The Hunger Games (Chapter 2)
Victors’ names are not put into the reaping balls again after they win their Games (except of course for the 75th Hunger Games), so they would not be eligible to volunteer.
“But never that I myself would have to be a player in the Games again. Why? Because there’s no precedent for it. Victors are out of the reaping for life. That’s the deal if you win. Until now.”
- Catching Fire (Chapter 13)
Volunteers must be eligible to compete in the Games themselves. This becomes even more clear in the case of the 75th Games, when victors are the only ones eligible to compete.
“Without hesitation, he reads, “On the seventy-fifth anniversary, as a reminder to the rebels that even the strongest among them cannot overcome the power of the Capitol, the male and female tributes will be reaped from their existing pool of victors.”
- Catching Fire (Chapter 12)
The only ones eligible to volunteer for the 75th Hunger Games are previous victors. Only a victor could step in to take the place for one of the victors chosen.
“Brutus, a volunteer from District 2, who must be at least forty and apparently can’t wait to get back in the arena. Finnick, the handsome bronze-haired guy from District 4 who was crowned ten years ago at the age of fourteen. A hysterical young woman with flowing brown hair is also called from 4, but she’s quickly replaced by a volunteer, an eighty-year-old woman who needs a cane to walk to the stage.”
- Catching Fire (Chapter 14)
So Haymitch could volunteer for Peeta, and Peeta could volunteer for Haymitch, but no one else could volunteer for either of them because they were the only two living male victors from District 12. No one was eligible to volunteer for Katniss, because she was the only living female victor from District 12.