There's a fish the princess mentions having had a childhood crush on, and there's a guy who shows up later in the story that's got some chemistry with the princess and the potential to eventually become a love interest, but I doubt the writer's going to take it in that direction because the core concept of "the mermaid princess eats another fish every week" doesn't really improve that much by adding romance.
@Agni
because the manga try to show they are sentients creature able to think and marry and care for their children
because sea creature in real life are bunch of cannibals who'll eat even their children because they can't distinguish that they are their children also brothers and sisters eat each others since birth
also most of them don't marry but drop their things on water (if you know what i mean ) until they meet to form a fertilized egg