Gronkowski has practiced the past two weeks, but has not been cleared to play as he recovers from back and forearm surgeries.
Gronkowski has not played since he was injured in the regular-season finale in December 2012. He missed five games last season between Nov. 22 and Dec. 23 with a broken forearm. He had multiple forearm and back surgeries in the offseason.
According to ESPN, Gronkowski's inner circle of friends and family want assurance he is fully recovered before he plays again.
His $3.75 million (£2.32 million) salary for next season is guaranteed, as well as his $250,000 off-season bonus. In 2015, his $4.75 million (£2.94) salary is guaranteed for injury only. He also has a $250,000 (£154,000) off-season bonus.
As for Amendola, he said he feels like he is "really close" to being ready to return from a groin injury. The Patriots are being cautious as he has a history of leg injuries.
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Chicago Bears cornerback Charles Tillman is expected to play on Sunday against the Detroit Lions.
Tillman is listed as questionable with knee and groin injuries, but the NFL Network reported on Saturday that he will play.
Bears coach Marc Trestman said he was "reasonably optimistic" Tillman would play.
Tillman, 32, has 14 tackles and two interceptions this season. He has not missed a start since 2009. He missed practice on Wednesday and Thursday, and returned on a limited basis on Friday.