I see a lot of people guessing that Iron Bull and Varric will be the race gated ones, but I feel a little doubtful. I don't really think they'll both be LIs. It's possible, but I think the gender numbers will be more even. There are four females that are probably open to romance. It's possible there are some we don't know about, but I believe they'll stick with companions and advisors as what they consider full romances. So, I think there will be 3-4 female romances and 3-4 male romances. For the males..
Cole - All but fully, undeniably confirmed he wont be a romance. HEAVILY implied not to be.
Blackwall - It's possible he is, but I think he's probably too old and close to his calling.
Cullen - Confirmed to be an LI.
Dorian - He most fits the standard for an LI out of all the companions. I will be very surprised if he's not a romance for SOMEONE.
This is the group I'm on the fence about --
Solas - We really know very little about him. People will assume he is going to be, because he's the only male elf and that's popular. He's been very popular with the female demographic and I know a lot of girls will be disappointed if he's not available. What makes me uncertain is that we just know so little about him that we can't be sure there isn't a strong reason why he wouldn't be a romance.
Iron Bull - A lot of people have assumed he's an option because of the comments that he'll have sex with anyone. I'm still really uncertain, because he is still a "real" Qunari. Establishing a relationship is against their philosophy. What would happen if he did? Would he have to leave the Qunari? Would he have to try to hide it? Would it even be something he wanted to do? I still wouldn't be surprised if he was just a fling or even not available, but I'm also not totally willing to rule it out.
Varric - I have a hard time not seeing Varric as straight after DA2, but I also have a hard time seeing them give the straight females a dwarven, restricted character as their "exclusive". Most people play humans and he would be restricted from humans? But I also don't feel confident that they'll be adding an extra, hetero exclusive to females on top of Solas, Cullen, or whoever else it is. It's more just that I don't think they'll be pushing the numbers that high. It's possible he could be bisexual. It wouldn't be the first time a character only showed interest in one gender, was vocal about that interest, and then turned out bi later. (ilu Anders) I don't think they'll do two race gated bi male companions, though, so I feel like it would be either Varric or Iron Bull and not both. With the hints we got before about Bianca maybe still kicking around, I think Iron Bull may be more likely, but I guess we just have to wait and see.
I realize I'm making a lot of assumptions here, but that's all we really have right now. 