When we saw the fourth episode she asked him “What do you think, I should do”?, “I’am at war and I’m losing”. He answers it in a way, that he is more inclined towards the good of all people in the seven kingdoms and safety of the realm. In the fifth episode when daenerys returns, after burning alive the Tarly. She sees that the dragon gets near to Jon snow and stops snarling, when he rubs his hand on its cheek . And when he says he is going to lead a raid in the north. She gets astonished by his decision, to head north of the wall, being a king in the north. Because there is a grave danger out there, and he could have sent his men instead. the way he convinces her is quite impressive. I mean “trust in a stranger”.
In the sixth episode, when Jon snow returns, he is brought on to the Targaryen sails and when Ser Davos removes his clothes, she sees that Jon snow have a few stabbings on his chest and heart. She realizes that the words from Ser Davos mouth in the third episode, weren’t any northerners flights of fancy, as Tyrion said, but it was true.
All these reasons, explains that she admires Jon snow, the way he is king-king and to the extent he goes for anyone, who trusts him.
And it can also be like this, when she asked Ser Barristan Selmy about Rhaegar Targaryen (her brother), in the fifth season.
Ser Barristan Selmy told Rhaegar Targaryen (Jon’s dad) was a very good prince of his time and was a great singer and the people who followed him, believed in him and his cause for fight. May be seeing jon snow, daenerys thinks of her brother. (OR)
When the Red Priestess of Asshai “Melisandre” arrives at Dragonstone. She says the lord of light has promised a prince/princess who would save the realm, from white walkers. She also says that the prince/princess might be Daenerys or Jon snow. So may be she thinks that Jon snow is the prince, gods have promised, as he was fighting for the realm for a good cause.
Apart from that, Daenerys loves Daario Naaharis and i think he is still alive out there.
Even if they are in love we already know that the Targaryen siblings are naturally attracted towards each other and always end up experimenting sexually.
So, Aunt is not a big deal. “sorry just joking“.
It will not be like that, but if it is, then it will be quite depressing.