"We're deeply committed to getting Jamie back in here and on the ice in time for the weekend," Gaglardi said. "I know that Joe and his group are talking daily with Jamie and hopefully making progress.
"We're deeply committed to having Jamie here in a Dallas Stars jersey for a long, long time. He's a key part of our future. Hopefully, we're going to have some good news in the next few hours regarding that."
Benn, 23, is believed to be looking for a multi-year contract worth in the neighborhood of $5.5 million per season.
According to TSN's Bob McKenzie, Benn wants a deal in between three-to-five years.
"Jamie Benn's agent Rich Evans says his client has no interest in a six-year deal and would prefer 3 to 5 years for term," McKenzie tweeted this afternoon. "Still working on it."
In 71 games with the Stars last season, Benn registered a career-high 26 goals and 37 assists for a total of 63 points, a seven-point jump over his 56-point total in 2010-11.
Benn's three-year, entry-level contract expired last summer.
The native of Victoria, B.C., was originally drafted by the Stars in the fifth-round (129th overall) of the 2007 NHL Entry Draft.