Burgess, originally drafted by the Eagles in 2001, returned to Philadelphia on Tuesday after being out of the NFL this season. He was released by New England before the season.
The 32-year-old Burgess has 52 career sacks, including a league-high 16 with Oakland in 2005.
Graham, the 13th overall pick in this year's draft, tore a right knee ligament in Philadelphia's win at Dallas last Sunday.