Bradford suffered a concussion and shoulder injury during the defeat to Miami Dolphins last weekend and was replaced in the Eagles lineup by Mark Sanchez for the defeat to the Tampa Bay Buccaneers on Sunday.
According to NFL Network, Bradford is expected to sit out the clash with the Detroit Lions on Thursday, and his long-term future at the franchise could be in doubt.
The report claims that Sanchez will again start in what has become a 'two-game audition' to become the club's starting QB, and suggests that Bradford's failure to sign a contract extension could see Philadelphia ditch him as their first choice.
The site's reporter Ian Rapoport said: "It is not like the Eagles can say 'we have invested a ton of guaranteed money in Bradford, he is for sure our starter.'
"If Sanchez plays well enough to, say, win two games, it seems as if the team would continue to use him as the starter going forward.
"Then, this offseason, with seven college quarterbacks rated in the first three rounds, the Eagles will once again be exploring the quarterback market."
The Eagles have started the season 4-6 and are currently third in the NFC East.