The team also has released veteran linebacker Lawrence Timmons, who signed with the team last offseason.
The Dolphins likely will make the move on Suh on Wednesday, sources said.
Suh might have hinted at the upcoming move when he tweeted a video Monday morning in which he said "There will be some exciting things going on."
The Dolphins are moving on from Suh and Timmons as they continue their attempt at a culture change -- a plan that already led to the trades of wide receiver Jarvis Landry last week and running back Jay Ajayi in October.
Suh's release also will take a large contract off Miami's books. Suh carried a salary-cap number of $26.1 million for the 2018 season, including a base salary of $16.985 million.
If Suh is designated as a post-June 1 cut, the team would save $17 million against the 2018 salary cap. Releasing Suh now would save the Dolphins just $3.9 million against the cap.
Timmons' release leaves $7.25 million in dead money on the team's salary cap.
Suh, 31, never hit the heightened expectations that came with the six-year, $114.4 million contract he signed in 2015. He has made just one Pro Bowl over the past three seasons and has not totaled more than six sacks in a season.
He has never won a playoff game, and with him last year, Miami finished 29th in run defense and 26th in sacks. He had 4½ sacks and 48 tackles for the Dolphins, who went 6-10.
Timmons was suspended one game by the Dolphins last season for after he went AWOL a day before the team's opener in Week 2 against the Los Angeles Chargers. The Dolphins' Week 1 game against the Tampa Bay Buccaneers was postponed until later in the season because of Hurricane Irma.
The Dolphins located Timmons before the game against the Chargers but made him inactive, snapping his streak of 101 consecutive starts. He was suspended for the following game, against the New York Jets. He finished the season with 84 tackles in 14 games.
With the Detroit Lions, who selected him No. 2 overall in 2010, Suh was a dominant force in the middle for five seasons, making the Pro Bowl four times and being named first-team All-Pro three times. He played in 78 of 80 regular-season games for Detroit while making 238 tackles with 36 sacks, 13 pass breakups, two forced fumbles, a fumble recovery and an interception.
Suh has a history of being fined for player-safety violations. The only two games Suh missed in his career were due to a suspension after he stomped on then-Green Bay Packers offensive lineman Evan Dietrich-Smith in 2011. Suh was initially suspended for Detroit's playoff game against the Dallas Cowboys in 2015 before his suspension was overturned and replaced with a $70,000 fine for stepping on the calf and ankle of Packers quarterback Aaron Rodgers.
Timmons, 31, signed a two-year, $12 million contract with the Dolphins last offseason, leaving the Pittsburgh Steelers after 10 years with the team. He recorded 677 tackles and 35.5 sacks during his time with the Steelers.
The Associated Press contributed to this report.