Romo has already received strong interest from television networks that want him to work as a color analyst but he wants to play, league sources told ESPN's Adam Schefter on Sunday.
Romo, who turns 37 in April, is owed $14 million next season and carries a $24.7 million cap hit should the Cowboys decide to keep him. A team trading for Romo would be responsible for his full 2017 salary.
Romo missed 12 games in 2015 with a broken collarbone and then missed the beginning of this season after a preseason back injury, losing his starting job to rookie sensation Dak Prescott, who led the Cowboys to a 13-3 record and the No. 1 seed in the NFC playoffs. Prescott, 23, was named the Associated Press' NFL Offensive Rookie of the Year on Saturday after passing for 3,667 yards and 23 touchdowns with just four interceptions this season.
Romo missed the Cowboys' first 15 games and appeared in only one game, completing 3 of 4 passes for 29 yards and a touchdown in a 27-13 loss to the Philadelphia Eagles on Jan. 1 in the regular-season finale.
Cowboys owner Jerry Jones said last month that Romo will play in a Super Bowl before he retires and believes the four-time Pro Bowl quarterback is still capable of playing at the level of Aaron Rodgers, who threw for 356 yards, two touchdowns and an interception in the Green Bay Packers' last-second 34-31 win over the Cowboys in the NFC divisional playoff game.
Romo is the Cowboys' all-time leader in passing yards (34,183) and touchdown passes (248).