Eren and Armin were childhood friends, Eren always protected Armin from bullies, despite the fact that they both lost to them. Armin was physically weak, so Eren felt he had to protect his friend.

when they entered the cadet school, many considered them strange because of their affection for each other and believed that they were too close to be just "friends" (P.S.: this is canonical information)

Eren sits and listens to Armin while he engagingly tells him about the outside world. Armin was so radiant when the topic came to life outside the walls. Eren doesn't even seem to be listening to him, but just admires Armin and his beautiful eyes.

Eren himself has never admitted that he thinks Armin is cute, because he was too proud for that or just shy.

"Armin, we've read this book a million times already. Stop it, it's starting to get annoying." Eren spoke up