Walker was released by the Tennessee Titans in March after seven years with the team. The 35-year-old earned three Pro Bowl selections from 2015-17.
The Patriots are especially thin at tight end after Matt LaCosse decided to opt out of the season, per Michael Giardi of NFL Network. Ben Watson also retired after last season
New England has rookie third-round picks Devin Asiasi and Dalton Keene capable of filling in next season, but the team could instead use someone with more experience like Walker.
The Central Missouri product appears to have options, however, even after two injury-filled seasons. Walker finished 2019 with 21 catches for 215 yards but was held to just seven games before going on injured reserve with an ankle injury. An ankle issue also ended his 2018 campaign after just one game.
Tennessee decided to move on in the offseason with Jonnu Smith emerging as a reliable weapon.
In 14 years in the NFL, Walker has topped 800 receiving yards in four seasons. He was effective in 2017 with 74 catches for 807 yards and three touchdowns.
Teams could be looking for a bounce-back performance if he can remain healthy, with the Patriots and Ravens two of multiple organizations kicking the tires on the California native.
Matt Barrows of The Athletic reported on July 28 that the San Francisco 49ers were also interested. In March, the Washington football team, Green Bay Packers and Indianapolis Colts were among the teams putting him on their radar, per John Keim of ESPN.
With training camps underway, organizations are looking to fill the holes on their rosters and could be ready to add a key veteran like Walker.