Sources told the NFL Network that Flowers and the Lions agreed to a five-year contract worth more than $16 or $17 million per season.
Deals can't be finalized until the NFL's new league year, which begins Wednesday. Teams could begin to talk with free agents Monday.
The pending acquisition of the 25-year-old Flowers would reunite the pass rusher with Lions head coach Matt Patricia. Patricia served as Flowers' defensive coordinator with the Patriots for his first three seasons.
New England drafted Flowers in the fourth round of the 2015 NFL Draft. In four seasons with the Patriots, he has 164 tackles and 21 sacks. He had 9.5 sacks last season.
Sources told the NFL Network that the Lions also agreed to terms with cornerback Justin Coleman on a four-year deal worth $36 million. Sources informed the NFL Network that Detroit remained active Monday and reached a deal with former Pittsburgh Steelers tight end Jesse James.
Coleman has 126 tackles, three interceptions, two defensive touchdowns, two sacks and 27 passes defensed in four seasons between the Seattle Seahawks and Patriots.
James recorded 120 catches for 1,189 yards and nine touchdowns in four seasons with the Steelers.