The veteran gunslinger is interested in signing with the team and the Cowboys are also interested in bringing him onboard as a backup to Dak Prescott, according to ESPN's Ed Werder.
Werder tweeted about the "mutual interest" and said that a Romo decision "must come first."
The Cleveland Browns cut McCown on Feb. 7 after two seasons with the team. He completed 276-of-457 passes for 3,209 yards, 18 touchdowns, and 10 interceptions for the Browns. McCown owns a 2-20 record as a starter in his last three seasons.
The 37-year-old has played 14 seasons for the Arizona Cardinals, Detroit Lions, Oakland Raiders, Carolina Panthers, Chicago Bears, Tampa Bay Buccaneers, and Browns. McCown was due $4.375 million this season.
The 36-year-old Romo continues to be the hottest topic in free agency.