I'd love to see Varric as a romance. He'd absolutely be my favourite option, and if I had to (for the first time in any game ever) play through as a dwarf to see it, I totally would! I'm pretty much a lurker in this and the Varric threads and I'm loving your posts in both threads, Natashina 
But I'm conflicted - there are decent reasons both for and against the likelihood of his inclusion
Against: Cameron Lee's comment that he 'may not be ready to let go of Bianca' would seem to indicate that there's a Varric/Bianca storyline there rather than a Quiz/Varric one - and the fact that Varric still refuses to let that crossbow go throughout DAI (can't use any other type of ranged weapon) suggests that Varric still has strong feelings for his ex, still not sure about that as a basis for future romance, though I do like the story ideas about the Carta.
Didn't DG state (ages ago now, and I can't remember where) that he doesn't like the idea of dwarf romances? I know he isn't Varric's writer, and he may have changed his mind, but as lead he may have some influence here. Also, so few players go dwarf that Bio may not consider it worth the resources (assuming he's racegated to dwarves, this is) 
Depending on what we did with the red lyrium thingy in DA2, we don't know how Varric may have been influenced by that. It doesn't necessarily mean anything, but it could be a complicating factor in a romance.
For: Varric has a sizeable (and very lovely and polite imo) fanbase who were already disappointed in DA2. After all, BioWare made Garrus a romance after it became clear he was popular (even though he was also a 'bro' character) and the romance was very well-received, so it's not out of the question they'd respond to the fans in this way again.
Maybe the fact that so few players currently create dwarf characters works in Varric's favour - if it acts as an encouragement to do so (as it certainly would with me) then that's a good thing as it gets more players seeing the content that BioWare makes, further justification (if any were needed) for including race selection.
There has never been a dwarf LI before, and all the other playable races are already represented as romantic interests. 'Twould only be fair! 
Edit: Also, I'm pretty sure the Varric/Bianca storyline can be wrapped up early doors in a way that still allows for Quiz/Varric stuff. We are talking about a 100 hour game, after all!
So yeah, my heart says Varric (straight or bi, dwarf only) and Solas/Blackwall (bi, no racegate) or Viv with the extra racegate coming from within the romances we already know about (no dwarves for Cullen??) but my head is kinda saying Solas and Vivienne (racegated, but no ideas, really. No elves for Viv?) For now, I'm going with my heart and staying hopeful. Varric ftw!