By using the tender, the Patriots will keep the running back on its roster if he fails to find a new team by July 22.
The tender is worth $2.1 million, or 110 percent of the value of his 2016 salary with the Super Bowl champions, according to NFL Network.
Sources told ESPN that Blount was the only player in the NFL to get the May 9 tender.
The Patriots had a deal on the table for the 30-year-old at one point this offseason, but Blount declined to accept it. The franchise has since given an extension to James White and signed Mike Gillislee and Rex Burkhead. It also has Brandon Bolden, Dion Lewis and D.J. Foster on its depth chart.
Free agent Christine Michael was in Foxborough on Tuesday to visit the Patriots.
According to the rules regarding a May 9 tender, only the Patriots can sign Blount from July 22 through the Tuesday after Week 10 this season. If he signs with another team before July 22, the transaction could reward the Patriots with a compensatory draft pick.
Wednesday was the first day that free agents, who didn't return to their most recent team, could sign with a new franchise without influencing its formula for compensatory picks.
Blount led the NFL with 18 rushing touchdowns in 2016. He also ran for 1,161 yards.