The Cowboys are motivated to sign Romo because the player's salary-cap charge will double from $8 million this season to $16 million next season, the source said. Romo's contract is set to expire after the 2013 season.
The 32-year-old Romo, though, has not shown a great sense of urgency this season to re-sign. He believes he is leading a strong Dallas team that is capable of winning into the postseason and thinks he can enhance his leverage when negotiations turn more serious, the source said.
Speaking Thursday about his contract situation, Romo said, "I haven't even thought about it."
Information from ESPNDallas.com's Todd Archer was included in this report.