"It's possible," Lions coach Jim Schwartz said Monday.
Stafford's right knee was twisted on a sack in the fourth quarter of Sunday's loss against the Chicago Bears and he immediately grabbed behind it and screamed in pain on the ground.
"He's day to day and we'll know more on Wednesday," Schwartz said.
Stafford suffered a subluxation of his right knee in which his kneecap popped out of its normal position but popped back in, a Lions source told ESPN senior NFL analyst Chris Mortensen. Sources said such an injury is not normally a season-ender.
One medical source even suggested that Stafford could play this week with a brace, but that will be determined by the pain and stability of the knee. He also could miss a week or longer.
Stafford will get a second opinion of the MRI on his knee from Dr. James Andrews in Alabama, sources told ESPN NFL Insider Adam Schefter on Monday.
Schwartz stuck by one of his policies, limiting information he shares about injuries, by declining to say if Stafford's kneecap is dislocated.
"You know my philosophy on injuries as far as commenting on specifics and things like that," he said.
Schwartz did acknowledge tests have been completed on Stafford's knee.
"It's just how he responds to it," Schwartz said.
But even if Stafford can't practice after Tuesday's off day, Schwartz insisted that wouldn't necessarily rule him out.
"I wouldn't want to put that set of rules out there before him," Schwartz said.
Daunte Culpepper replaced Stafford at Chicago and would likely start Sunday at home against the defending champion Steelers (2-2) if the rookie can't play.
Stafford wasn't in the locker room Monday when it was open for the media, but he told reporters Sunday the same knee was injured in high school.
"He hurt it in a freak accident on a Slip 'N Slide," his father, John Stafford, said Monday night. "After a hot day of working out in the summer with the football team going into his senior year, the guys were messing around on a Slip 'N Slide and he got hurt."
Stafford also suffered a similar injury at the University of Georgia.
John Stafford said his son sent him a text message Sunday, letting him know he hurt his knee and would have an MRI.
"I don't know anything more, but I usually don't get much out of Matthew," he said.
The Lions (1-3) did not respond too well to snapping their 19-game losing streak, losing 48-24 at Chicago.
"A couple of you astutely observed that I seemed a little ticked off after the game," Schwartz said at his weekly news conference. "And I'm here to say that after 24 hours, I'm probably more ticked off now than I was right after the game.
"We never gave ourselves a chance to win that game. There were way too many errors in all phases of the game, but particularly in special teams."
"He was behind in training camp, but our inefficiency in kick returns is glaring and it needs to be addressed," Schwartz said. "He's going to have to do the job for us."
The first-year head coach, though, does not plan to shake up his staff.
"I'm not George Steinbrenner," Schwartz said.
Information from The Associated Press and ESPN senior NFL analyst Chris Mortensen was used in this report.