Fairley, 27, was drafted in the first round by the Lions in 2011 and has spent the last four seasons in Detroit.
According to the Free Press, the Lions were in discussions with Fairley's agent on Tuesday but did not come to an agreement before the beginning of free agency at 4 p.m. ET.
The Free Press also reports that Fairley has received interest from "about six teams" and will visit the Cincinnati Bengals on Wednesday.
Fairley was limited to eight games last season due to sprained ligaments in his knee, and he recorded 14 tackles and 1.0 sack.
In 2013, Fairley started 15 games and had 35 tackles, 6.0 sacks and two fumble recoveries.
Detroit is losing defensive tackle Ndamukong Suh to the Dolphins, who will reportedly sign a six-year deal with Miami. On Tuesday, the Lions acquired defensive tackle Haloti Ngata in a trade with the Baltimore Ravens.
- Molly Geary