The 39-year-old Gonchar played the past three seasons for Ottawa, recording 15 goals and 76 assists. He has played 1,177 games in 18 NHL seasons.
Gonchar, whose veteran presence on the Senators' blue-line helped offset the loss of Erik Karlsson for much of the regular season, was reportedly seeking a multi-year deal.
Reports indicated he was considering signing in Russia's Kontinental Hockey League.
Gonchar completed the final season of a three-year, $16.5-million contract. His cap hit was $5.5 million.
If Gonchar signs with Dallas, it will be his fifth NHL team. The sixth-round pick is conditional on Gonchar signing a contract with the Stars.