I think Son Goku would consider Superman a great training partner. He'd probably help him burst through a few more limits.

In Superman canon, is there any amount of energy blast that can hurt him? Could an energy blast that covers the full spectrum mimic the mechanism of kryptonite that causes harm to Superman? Or physical force? If the answer to those is no, then that eliminates most of Goku's arsenal.

But the one that it doesn't eliminate might do the trick: instant transmission. Would Superman still be as strong and immune to damage if he was suddenly fighting Goku on King Kai's planet, without Earth's yellow sun? Would Goku even think of that strategy? Would he use it if Superman wasn't trying to destroy Earth, even if he did know that weakness?

And on the other end, would Superman fight Goku? Goku would definitely fight him, but Clark Kent isn't exactly an aggressive guy from what I know about him. Goku isn't like Vegeta in that he'd put people in danger to convince a hero to fight him. He might nag or beg or maybe even start a rumour that he is dangerous to get Superman to fight him on his own terms similar to how he hired Hit to kill him.

And even if Goku can convince him to spar, I don't think Superman will be willing to go all out unless Goku can actually push him that far. Like Gohan could have beat Goku at the Cell games but he would have never gone all out to get to that point, so it seemed like Goku was the stronger fighter by default until Cell did get him to go all out. And even that's not the full story because Goku then came back and surpassed Gohan again. And then Gohan has since shown that he still has more potential and who knows which one will be stronger if he hits that potential.

Superman would concede the fight before letting it get to the point of risking the destruction of Earth (let alone the universe). So then the question becomes, is Superman strong enough to destroy the universe if paired against an equal strength? With the way power scales in his universe, I don't think so. Goku and Beerus were headed towards that before Goku figured out how to nullify Beerus' attacks rather than power through them. And on that note, what does "god ki" mean in the context of Superman's universe? Hell, it's not very well defined in Goku's universe. Is Golden Frieza using god ki? Hit? Brolly? Each of them were able to pose a threat to Goku, so if they weren't using god ki then it doesn't matter if Superman can or can't.

Anyways, ultimately, as others have said, it comes down to what the writers of such a fight want because neither really exists and both are always as strong as they need to be for the current plot.

Maybe Goku instant transmissions them to Kai's planet but then Superman, after being easily beaten there, decides to stay and train, learning kaio-ken and spirit bomb. Then he returns and the fight becomes whether Goku or Superman has more fans to feed a spirit bomb to throw at the other. And I can only guess at who would win that.