De Sciglio has definitely been ruled out of next Wednesday's tie at the San Siro after suffering a knee injury in training on Monday.
The young full-back will require surgery on the problem and reports in Italy claim De Sciglio could be sidelined for around two months.
Abate will face a race against time to be fit to tackle Celtic after picking up an adductor problem while on international duty with Italy.
Milan expect the defender to be out for between eight and 10 days, making him a huge doubt for the visit of the Scottish champions.
The double injury blow leaves Milan coach Massimiliano Allegri with a selection headache as Cristian Zaccardo is now his only fit senior full-back.