Theo was in Paris on Friday to undergo a medical with Al-Hilal medical officials.
L'Equipe says Milan have accepted a €30m offer from the Saudis for the left-back.
For his part, Theo will earn a staggering €20m-a-year - tax free - on a multi-season contract with Al-Hilal.
The defender also had agreed personal terms with former club Atletico Madrid this month, but a fee couldn't be settled with Milan.