Yes, there are some. In some fanfictions, they might start as rivals but gradually develop a deep bond that could be interpreted as love. However, these are often very creative interpretations that deviate from the original animé's more straightforward rivalry theme.
You can try some popular fanfiction websites like Archive of Our Own (AO3). It has a large collection of fanfictions from various fandoms, including Dragon Ball where Goku and Jiren are from. Just use the search function and type in relevant keywords like 'Goku Jiren love' and you might find some interesting reads.
In this fanfiction, Goku vs Jiren is likely to be an epic battle. Goku's power with the Universe's Watch might bring new and unexpected abilities. Jiren, on the other hand, is an extremely powerful opponent. The fight could involve intense energy blasts, high - speed combat, and strategic maneuvers. It might also explore the growth of Goku's character and his newfound power in relation to Jiren's unwavering strength.
Another possible main character could be the villain that forces the two Gokus to meet. This villain could be a new, super - powerful threat that the two Gokus need to deal with. Their meeting becomes a crucial part of the story to defeat this powerful foe.
In the fanfiction, the plot could develop such that the power of the universe's watch attracts other villains or powerful beings. They might try to steal the watch from Goku during his battle with Jiren. This would add a new layer of complexity as Goku has to fend off these new threats while still trying to defeat Jiren.
Well, it could be about Goku Jr learning some of Goku's most powerful moves. Maybe Goku teaches him the Kamehameha. They might also go on an adventure together, like fighting a new and powerful enemy that neither could face alone.
There could also be a moment of self - discovery for both of them. Goku might see his past self in Kid Goku and realize how far he has come, while Kid Goku could get a glimpse of his future potential through meeting his adult self. They could share stories about their friends and enemies, like how Goku could talk about Vegeta and Frieza to Kid Goku, and Kid Goku could tell Goku about his early battles with the Red Ribbon Army.