If they are put in a situation where they have to protect someone or something together, like a group of innocent people or a powerful artifact. During this, they would start to communicate more, understand each other's motives better. For example, Goku's motivation to protect the weak might rub off on Turles, leading to a change in his attitude towards others.
Their relationship could develop through mutual respect for each other's strength. Goku, being the pure - hearted Saiyan he is, might start to see that Turles has potential for good deep down. Turles, on the other hand, could be in awe of Goku's power and gradually change his view of Goku from an enemy to a rival and perhaps even a friend.
Another way their relationship could develop is through training together. They are both Saiyans and love to fight and get stronger. By sparring and training side by side, they could learn from each other's techniques. Turles might teach Goku some of the more underhanded Saiyan tactics he knows, while Goku could show Turles the value of fighting with honor. This exchange could lead to a deeper bond between them.