Griffen and the Detroit Lions face the Vikings on Sunday.
The former Vikings star was traded to Detroit for a fifth-round pick.
Griffen has reportedly expressed interested in signing with Green Bay.
Hunter's name appeared on the NFL's transactions report on Friday.
The veteran lineman opted out of his contract and became a free agent last week.
ESPN's Courtney Cronin reports that Griffen could still return to the Vikings.
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Griffen had 5.5 sacks in 11 games last season.
Griffen was honored by the Vikings with the Ed Block Courage Award.
The Vikings haven't had Griffen in the lineup since Week 2.
Cook has been plagued by a hamstring injury since Week 2 at Green Bay.
There are some talented veterans available as free agents.
Griffen is not with the team for Thursday's game in Los Angeles.
Griffen agreed to have a mental health evaluation, according to police.
Multiple reports say Griffen is dealing with a serious personal health-related matter.
Griffen has a knee injury and Cook is dealing with a hamstring issue.
He's had a sack in every game this season, but now his mysterious injury is concerning.