Wayne said in July he wants to play at least one more season.
The Patriots are dealing with injuries to many of their wide receivers. Julian Edelman, Aaron Dobson and Brian Tyms have all missed a portion of training camp, while Brandon LaFell is still on the physically unable to perform list.
Wayne, 36, would be competing with fellow veteran Brandon Gibson and others for a roster spot if he signed with New England.
Wayne is the NFL's active leader in receptions and receiving yards, and is third in touchdowns. Last season, he caught 64 passes for 779 yards and two scores.
After playing in all 16 regular season games in 11 straight seasons, Wayne has battled injuries the last two years, playing in only 22 games.
For his career, Wayne has 1,070 receptions for 14,345 yards and 82 touchdowns.