League sources told ESPN's Adam Schefter that New England intends to keep the 25-year-old Garoppolo for 2017 and possibly beyond.
The Cleveland Browns, Chicago Bears, San Francisco 49ers and New York Jets were all were mentioned as being interested in trading for Garoppolo, who has one year remaining on his rookie contract with a base salary of $820,077 in 2017.
Starting quarterback Tom Brady is showing no signs of decline as he turns age 40 in August.
Brady, with five Super Bowl rings, has made it clear he has no plans to retire and wants to keep playing into his mid-40s after his record-setting performance in Super Bowl LI.
With Brady suspended for the first four games of the 2016 season over Deflategate, Garoppolo led New England to wins over the Arizona Cardinals and Miami Dolphins but suffered a right shoulder injury in Week 2 that knocked him out of the lineup.
Garoppolo played in six games in 2016, completing 68.3 percent of his passes for 502 yards with four touchdowns and no interceptions.