Sasuke was one of the first to acknowledge Naruto as a shinobi; not only did he state he wanted to fight him, he also admitted that Naruto was his best friend.
Naruto also strives to be just as strong as Sasuke; yes, they had a rivalry, but it was a healthy rivalry - they both push themselves and each other to constantly get better.
Also Sasuke wasn't as prejudiced as the village. When he called Naruto an idiot, it was because he was acting as an idiot. It would have been worse if he called him a monster - following the example of the village - but he didn't. And that's something I think Naruto appreciates because Sasuke was one of the few who didn't want to avoid him or call him a monster.