"Rob has quite severe ligament damage and we are looking at another four weeks for him," Hancock told Leeds United's official website.
The 25-year-old Hulse was injured during the recent tour of Norway.
Hancock also advised about Stone, 34: "The op has removed the degenerative part of the tear. It could be eight weeks or probably a bit longer than that, but he can make a full recovery."
But 35-year-old keeper Neil Sullivan has responded quickly to treatment on his shoulder injury and may play some part in the pre-season friendly at Barnsley tomorrow.