The Liverpool Echo says the Reds will pay an initial sum of around £1million for the 17-year-old who has said his goodbyes to team-mates in Brazil.
The teenager is now Merseyside-bound to complete his medical with Liverpool officials expecting to formalise the move next week.
Liverpool have been in talks with the Brazilian club since the end of August and have now struck a deal to bring Pitaluga to the club.
Pitaluga's dual citizenship made the deal easier to complete for the Reds, with the shot-stopper able to move to Europe before his 18th birthday as a result of his German passport.
"I am very grateful to Fluminense," said Pitaluga. "I was 10 years at this club, from futsal, passing through [the youth ranks], until I reached the professional ranks.
"I have always been treated very well and had all the assistance necessary for my development, both personally and as an athlete.
"This opportunity that came up will be very important to me. It was a unique opportunity, mainly for having a European passport."
Pitaluga was part of the Brazil Under-17 squad that won the World Cup in Brazil last year and becomes the second young shot-stopper to move to Liverpool this transfer window following Pole Fabian Mrozek.