Perhaps there could be a situation where the Sage of Six Paths in the Naruto universe senses Saitama's power from another dimension and pulls him into the Naruto world. Saitama is just looking for a worthy opponent and thinks he might find one here. Naruto and his friends initially view Saitama with suspicion. But as they see him take on powerful foes with ease, they start to trust him. They then join forces to stop an ancient evil that is about to be unleashed upon both universes. This evil has the power to nullify Saitama's strength and steal Naruto's chakra, so they have to find a way to defeat it together.
A plot could involve Naruto learning Saitama's training regime. Naruto is always looking for ways to get stronger. He might be intrigued by Saitama's simple yet effective training. Meanwhile, Saitama could be introduced to the concept of ninjutsu and start trying to learn some basic jutsus. However, his lack of chakra might make it very difficult for him, leading to some comical situations. And then they get pulled into a fight against a group of rogue ninjas who have teamed up with some One Punch Man villains.
One possible plot could be that Saitama somehow ends up in the Naruto universe. He might be mistaken for a very powerful shinobi at first. Naruto, being Naruto, would probably be curious about Saitama's strength and try to befriend him. They could team up to face a new, extremely powerful enemy that neither universe has seen before, like a super - strong demon that can absorb chakra and is also incredibly durable like the monsters in One Punch Man.