Endo set for 'dream' move to Liverpool from Stuttgart for £18.7m
Stuttgart head coach Sebastian Hoeness said that the defensive midfielder "had been cleared by the club for (contract) talks".
"He flew to England for a medical check and wasn't in training today.
"At the age of 30 he now has the opportunity to join Liverpool in the Premier League. It's a dream of his," Hoeness added.
German sports site Kicker reported Liverpool will pay approximately £18.7m for Endo, whose contract in Stuttgart was due to expire in 2024.
Endo comes as a surprising addition to the Liverpool squad, with new German sporting director Jorg Schmadtke the architect of the deal.
Liverpool have been on the hunt for a defensive midfielder since both captain Jordan Henderson and Fabinho made the move to Saudi Arabia in the summer.
The club's attempts to sign Brighton's Moises Caicedo and Southampton's Romeo Lavia failed. Caicedo moved to rivals Chelsea and Lavia is set to follow suit.
Hoeness said he was "not thrilled" with the loss of "an enormously important player" but explained "the economic package is good from the club's point of view".
"We will miss him."