He is expected to play next week, however, the source said.
Joique Bell and, potentially, rookie Theo Riddick are expected to see the majority of snaps Sunday in Bush's place.
Bush injured his left knee last Sunday when it collided with the helmet of Arizona Cardinalssafety Tony Jefferson during his 26-yard catch in the second quarter of Sunday's 26-21 loss. He grabbed it immediately, left the game and returned later.
After the game, Bush said he was cleared to return but didn't have the same explosiveness after he ran in the third quarter.
Coach Jim Schwartz has said he doesn't believe Bush's injury is serious.
"The tests today were encouraging," Schwartz said Monday. "He's going to be sore but he doesn't have anything that is going to be long term."
Bush had said Thursday he was "optimistic" he would be able to play but acknowledged that any decision on his availability would be a group decision instead of his alone.
ESPN NFL Insider Adam Schefter and ESPN.com Lions reporter Michael Rothstein contributed to this report.