In the movie Futari no Hero, Todoroki only stares at Momo in her yellow dress when she came through the door and did not look at any other girl but her. They also had a heart-to-heart conversation when training with Eraser Head in Season 2.
Does Todoroki like Momo romantically? I don't ship them, I just watch how the story plays out.
It's a possibility, but not one you could call obvious.
If you look at the characters, most of the boys and girls form some kind of pairing considering their friendships, which could evolve to romance. Kirishima with Ashido, Jiro with Kaminari, Hagakure with Ojiro. And of course, Izuku with Ochako, the one ship which is more probable to happen, considering Ochako's feelings have been shown openly to the reader.
But in the case of Momo and Shoto, they could very well be just good friends. Considering she is kinda the only girl he is close with, I don't consider it enough evidence. If we do, we could very well also ship Momo with Jiro too, just by that scene of Jiro blushing at seeing Momo's boobs.
According to this website (caution - contains a small spoiler):
Momo Yaoyorozu likes Todoroki; however, both of them are caught up in their own issues at the moment and do not have the time to engage romantically. As the series progresses, they might even end up together.
This is saying that Todoroki does not like Momo, but Momo likes Todoroki.
