The 2020 Comeback Player of the Year reportedly "would prefer to go to a place where he could compete for a starting job," according to Dan Graziano and Jeremy Fowler of ESPN.
Graziano and Fowler speculated the Chicago Bears or Denver Broncos as destinations, while the Seattle Seahawks and Houston Texans could also have openings if they trade Russell Wilson and Deshaun Watson, respectively.
Smith started six games for the Washington Football Team last season but was released in a move that saved the organization $14.9 million against the cap.
Washington went 5-1 in Smith's starts during the regular season, although a lot of that was thanks to a defense that finished fourth in the NFL in points allowed and second in yards allowed.
Smith finished 2020 with six passing touchdowns and eight interceptions in eight appearances, producing a 34.8 Total QBR that would be last in the league with enough attempts to qualify.
The 36-year-old still has room to improve as he gets further away from the devastating 2018 leg injury that kept him out for all of 2019. The three-time Pro Bowler has been a reliable player under center in the past, leading the NFL with a 104.7 quarterback rating in 2017.
In seven career playoff games, Smith has 14 touchdown passes and just two interceptions.
This experience could give the veteran another shot as a starting job going into 2021.