Although no official agreement has been finalized, Modric has expressed his commitment to joining the team after fulfilling his Club World Cup obligations with Real Madrid.
As Modric is contracted to Real until the end of the tournament, he will then enter into final negotiations with AC Milan.
Following this, he will undergo a medical examination and sign the necessary paperwork.
According to reports, Modric is willing to shorten his summer break to begin working with AC Milan coach Max Allegri and participate in preseason training.
Given the Club World Cup is scheduled to conclude on July 13, it's likely Modric will join the team at Milanello before the end of the month.