According to The Sun, Victoria Cross hero Beharry has been practising with the show's ice dance trainers.
The Lance Corporal, who twice rescued comrades while under fire in Iraq, has apparently been approached to "broaden the appeal" of the reality show.
"Johnson would be an exciting addition and bring a new dimension to the refreshed show," said a source. "The fact he is already highly regarded by the public helps. He is a very determined character.
"He's training despite being in pain from his injuries. If he copes well then he is a cert to appear in the final 12 in January."
TV presenter and actor Wilkes, 31, is also apparently trying out for the show.
Dancing On Ice will return for a sixth series in the New Year on ITV1.
> 'Dancing On Ice' venue changes confirmed