While nothing has been signed, Modric has committed to joining Milan once his Club World Cup commitments with Real Madrid conclude.
The veteran midfielder is contracted with Real to the end of the tournament, when he will immediately enter final talks with Milan ahead of taking a medical and signing forms.
And La Gazzetta dello Sport says Modric is prepared to cut short his holidays in order to get started with Milan and undergo preseason training with coach Max Allegri.
The Club World Cup ends on July 13, with Modric likely to be at Milanello before the end of the month.