Suh's departure would be the latest in cost-cutting moves by the Dolphins, who missed the playoffs in 2017 after finishing 6-10.
During the season, Miami traded running back Jay Ajayi to the Philadelphia Eagles - where he went on to win a Super Bowl title - while agreeing to trade wide receiver Jarvis Landry to the Cleveland Browns last week. The report has since been confirmed by a league source.
By designating Suh as a post-June 1 release, the Dolphins can save about $17 million against the cap.
Suh's release is not a complete surprise, but the timing was always in question.
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The Miami Dolphins' purge apparently will continue Monday.
The Suh decision comes roughly three years after they signed the defensive tackle to an enormous six-year, $114 million contract.
Despite his age and relative ineffectiveness over the last few seasons, Suh should have plenty of offers once released.
Suh accumulated 36 sacks during his five seasons with the Lions, three times going over eight sacks in a season. Suh teased some "exciting news" on Twitter on Monday morning, which would seem to indicate he knew this revelation would hit the National Football League news cycle today. So that video could have been a hint that he was no longer going to be with the Dolphins organization.