No, he can't. While some dragons had breath hot enough to melt the lesser rings of power, Gandalf says:
[...], nor was there ever any dragon, not even Ancalagon the Black,
who could have harmed the One Ring, the Ruling Ring, for that was made
by Sauron himself.
Adding source and larger quote for context.
It is established that Mount Doom is the only practical possibility. LOTR I.2 (when Gandalf verifies that Frodo's ring is the Ring and tells Frodo what that means):
But there is no smith's forge in this Shire that could change it at all. Not even the anvils and furnaces of the Dwarves could do that. It has been said that dragon-fire could melt and consume the Rings of Power, but there is not now any dragon left on earth in which the old fire is hot enough; nor was there ever any dragon, not even Ancalagon the Black, who could have harmed the One Ring, the Ruling Ring, for that was made by Sauron himself. There is only one way: to find the Cracks of Doom in the depths of Orodruin, the Fire-mountain, and cast the Ring in there.
(Several of the Seven were destroyed by dragons.)