The last Targaryens are finally going to meet in the next episode of Game of Thrones. After receiving a letter from Tyrion asking him to go to Dragonstone and "bend a knee" before Daenerys and another letter from Sam telling him there's a mountain of dragon glass at Dragonstone, it was pretty much a no brainer where Jon was heading. Though Daenerys and Jon are related, they have no idea. So will Jon and Daenerys get together on Game of Thrones? It's definitely a possibility.
Though Daenerys definitely doesn't need any more help securing the Iron Throne, having Jon on her side could definitely be an asset since he's King of the North. What better way to secure an alliance than with a marriage? It's what Cersei plans to do with Euron and Daenerys purposefully cut ties with Daario so she'd be able to make an advantageous marriage if need be.
Even if Daenerys doesn't consider marrying Jon, the pair could still end up hooking up. A private conversation about the future of Westeros and the White Walkers could easily lead to something more, especially because Daenerys seemed very interested in Jon.
"He sounds like quite a man," she said to Melisandre, during their meeting.
Some fans have been hoping Daenerys and Jon would hook up and even get married, while others can't get past the fact that Daenerys is Jon's aunt. Whether you ship it or not, it definitely seems plausible that something will happen between these two and very soon.
Though it'd certainly be interesting to see a romance form between Daenerys and Jon, they'll probably also butt heads over some key points. Daenerys' main focus is to take back the Iron Throne, while Jon's main focus is to prepare for the war against the White Walkers. It seems highly unlikely that Daenerys will care about the White Walkers and their oncoming march south, unless Jon can somehow prove what he's seen, which he can't.
All Daenerys will have is his word that this threat is headed their way, whereas Daenerys knows she must defeat Cersei to take back the Iron Throne. Why would Daenerys willing give up her resource of dragon glass to Jon Snow for a cause she probably won't believe in? It'll be up to Jon to make Daenerys believe him and even if she does, she'll definitely want something in return for that dragon glass. The only question is, what will she want?