The Belgian champions have revealed that they have been talking to the 16-year-old's 'entourage' for three months in bid to persuade them that the midfielder's best interests are served by staying in Brussels.
"The entourage of the player has decided to take the British club's offer", said Anderlecht sporting director Herman Van Holsbeeck who will negotiate the compensation due to his club.
"We now await news from Manchester," Van Holsbeeck told Het Belang van Limburg.
"For months now, we have been in meetings with the father of Januzaj to keep the player at Anderlecht, but at some point you cannot go any further."
Reports claim United have offered to pay the teenager a monthly salary of 10,000 euros and, although Anderlecht can claim a small training fee, they were powerless to prevent him from leaving because he had no contract.
"As a 16-year-old, it is the parents who decide," said Van Holsbeek. "We are obviously disappointed that he leaves, but the future will tell if the entourage of the player has taken the right decision."