If Mat and Perrin aren't bound to the horn, then I don't know who could be.

 

Seriously, those guys are obvious choices. They each have an interesting set of abilities that would give them the cool nickname/title that every Hero needs (Perrin Wolfbrother, Mat the Gambler or General or whatever), they've accomplished incredible things, and they're instrumental in the quest to save reality.

 

If they're not inducted, no one is.

Rand, Mat, and Perrin all seem to be. I can't be sure about Egwene, Nyn, etc, but there is a chance they are as well, but what is required to be a hero is truly extraordinary.

 

I suspect that Verin very well may have earned the right to be a hero, she risked her very soul to the shadow in order to turn at the critical moment and allow for the defeat of the black ajah and other darkfriend plots.

Like others, the other Light-sided characters I take are not reborns of Heroes.

Though there seems a chance of at least Perrin & Mat becoming Heroes. Possibly also Rand's 3 lovers. Perhaps Nynaeve & Lan. Maybe also Moiraine & Thom. and Noal. Like another, possibly Verin (she for the most part seemed Light-sided).

 

I recall from somewhere that the "key" for becoming a Hero is sacrifice. Do not remember the exact wording nor where.

Each the characters I mentioned seemed to sacrifice something.