The newspaper said Gradkowski had an MRI performed after re-injuring the shoulder during Oakland's 33-17 loss to Miami Sunday.
Gradkowski was making his first start since an Oct. 10 win against San Diego when he took a hit that aggravated the injury he first suffered in a Sept. 26 loss against Arizona.
He missed the next four games after the San Diego game and now in is jeopardy of missing the rest of the season.
He has completed 52.9 percent of his passes for 1,059 yards, five touchdowns and seven interceptions in six games this season.
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