Gonchar, who could be dealt by the start of the new season, has one-year left on his contract.
According to the Dallas Morning News, the Stars are willing to pay half of Gonchar's $5 million salary, but have not yet been able to find a suitor.
If Gonchar is dealt, he isn't expected to bring in a large return, which has Nill searching elsewhere for a defenseman.
Unrestricted free agent blueliner Michael Del Zotto is believed to be of interest, as several other teams are also eyeing him.
Del Zotto, 24, struggled this past season, having been traded from the New York Rangers to the Nashville Predators, who elected not to pitch him a qualifying offer.
He is coming off a two-year, $5.1 million contract. He's likely to sign a short-term deal worth an annual figure less than the $2.9 million salary he made last season.
Nill could look elsewhere, via the trade market, for a defenseman, but nothing is believed to be imminent.