Massimiliano Allegri's team are currently preparing to participate in the Audi Cup in Germany, and will travel to the United States for the International Champions Cup early next month.
But they will be without full-back De Sciglio after he suffered a twisted knee, while centre-back Mexes has been sidelined by a muscle strain.
Milan were also recently hit by the blow of losing Daniele Bonera for up to three months, with the 32-year-old having suffered a fractured kneecap in last week's International Champions Cup opener against Valencia.
However, Allegri can still call on the likes of Mario Balotelli, Sulley Muntari and Stephan El Shaarawy, with that trio among a strong squad named for the club's pre-season campaign.
The Serie A side's next fixture will come against Manchester City on July 31, as part of the Audi Cup at the Allianz Arena.
The Italian club will hope these fixtures can stand them in good stead for improving on last season's third-place finish in Serie A.
