No longer a theory, Jiraiya seems to know about the identity of adult Sasuke in episode 132 of the Boruto anime.
The problem is, how did Jiraiya find out Sasuke’s true identity?
1. Chakras
Although Jiraiya is not a sensing ninja, in the Naruto series, some powerful ninjas will be able to sense chakra from other ninjas.
2. Rinnegan Eye
When Sasuke first teleported time into the past and appeared in Konoha, he did not use the eyepatch.
3. Sasuke’s behavior
Jiraiya’s first suspicion probably stemmed from Sasuke’s strange behavior.
4. Appearance
Although Jiraiya did not often talk to Sasuke, he did meet him many times.
5. Dialogue with Naruto
At Jiraiya’s request, adult Sasuke came to give a small lunch box to Naruto, creating an opportunity for the two to talk.
Perhaps after watching the conversation between `uncle` Sasuke and young Naruto, Jiraiya’s suspicions increased.