No, Avowed doesn't have any romance options, but the game's director has some pretty good reasons behind the decision

Romance options are pretty popular in RPGs these days, and even though Avowed doesn’t have any, its director thinks it’s better off without one.

But one of next year’s biggest RPGs, Avowed, won’t have any romance options, despite it being a pretty common thing to find in the genre these days.

And so we felt that we could best tell our companions’ stories and our players’ relationships with them without the romance option.”