The Austria international player has been in Real Madrid’s sights for a while, with a previous bid of EU€50m rejected.
According to sources at Spanish site AS, Real Madrid upped its offer now to €65m. Bayern Munich has yet to respond to Real Madrid.
Alaba’s father is of Yoruba descent but relocated to Austria with his wife. Born in Vienna, 23-year-old David was the youngest ever person in history to play for the Austrian senior team in 2009 when he was 17.