It's believed the offer comes close to what Benn is asking for, which is reportedly around $5.5 million per season.
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.
It's not yet known when Benn and his agent, Rich Evans, will respond to Nieuwendyk and the Stars.
Meanwhile, Stars head coach Glen Gulutzan juggles the lines a little in camp today, as a result of Benn not being there.
"Playing without Benny could be difficult, but we're focused on the players we have here," Gulutzan told the Dallas Morning News. "Everything for Jamie is in place for him whenever he's here. But we're focused on the guys we have here."