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No, instead Jiraiya tells Naruto about Tsunade, as Naruto first met Jiraiya.
Jiraiya is Naruto's godfather and teacher.
He is Naruto's Godfather because Naruto's dad (Fourth Hokage)was trained with Jiraiya so that makes him his Godfather
Jiraiya kniws naruto but not really in his family no.
on Naruto's journey with Jiraiya when the last episode of Naruto appears and 2-3 years pass