...but don't rule out Jon Snow
Yes, Dany fits all the requirements, but Melisandre is fixed on Jon Snow. She has, of course, been wrong before. Her blind faith in Stannis Baratheon led to the unnecessary burning of his daughter Shireen, the decimation of his army, the suicide of his wife, and, ultimately, his death. Melisandre, so desperate for a Prince to follow, misread the signs – to the detriment of everyone who put faith in her fire.
But what if Stannis was only the conduit through which Melisandre would eventually find Jon Snow? In the fifth book, A Dance With Dragons, a frustrated Mel asks for a sign from her god. "I pray for a glimpse of Azor Ahai, and R'hollor shows me only Snow," she ponders. And yes, "Snow" is capitalized in the text, which seems like a pretty big wink from the holy R'hollor.
In the show, Jon is also, quite literally, reborn. It's hard to parse out what might be the salt and smoke (The fireplace? The potions Mel uses?) but again, those finer details might matter less than the actuality of his rebirth. Or perhaps we're talking about his first birth, to his mother, Lyanna, who died shortly after. On the show, when Ned arrives at the scene, he sets a sword at Lyanna's bedside: Arthur Dayne's sword, Dawn. Emblazoned on Dawn is a fiery star, to symbolize the falling star it was said to be forged from.
And if the popular R+L=J theory proves to be true, and Jon is actually the son of Rhaegar Targaryen and therefore part of his bloodline, this would make him – as a Stark/Targaryen – the "song of ice and fire" that Rhaegar spoke of in Dany's vision. Jon's also currently leading the fight against the White Walkers, just like Azor Ahai, and has an interesting dynamic with the Night King, who watched him with piqued curiosity at Hardhome. Does he sense a threat in Jon?