I have a feeling that, rather than this new dude being a 'potential romantic interest' (though either way I'm confident that we all know who she'll actually end up with - initial "V") the guy is just happens to be the squad's primary relationship gossip monger (and gossip monger in general). If so then he likely approached her due to the fact that she's the first woman Veramude's ever shown this degree of favour towards, and wants something more than mere speculation for the next gossip session with the other squad bros.
Of course I could be wrong and he might actually be romantically interested in her, but I feel like that would be too much of a stereotypical development, considering that this is one of the more progressive stories rather than merely a generic "elegant lady" or "poor girl" "meets strong and powerful man" or "meets strong and powerful men" "and he/they gets obsessed with her for whatever reason" or "she pulls his/their attention" story. Don't get me wrong; some of those are actually pretty decent. But they're still very typical and predictable examples of the romance genre.
PS: One of my favourite parts of this story is that the male lead doesn't have the archaic "she's so pretty I need to protect her" mindset, or anyone important spouting phrases like "you're still a young woman, just let me handle this" to a powerful Swordmaster or Mage.