Nill has seen how the saga with Steven Stamkos and the Tampa Bay Lightning has played out since last summer and doesn't want to risk the same thing happening with Benn and the Stars.
"I think it's important," Nill said. "We're going to start talking. We've got July 1 when we can start doing that. I think it's important. I know Jamie is staying. He's the captain of our team. We're going to get something taken care of and go from there."
Benn is entering the final year of a five-year contract. He told the Dallas Morning News in May that he wants to re-sign with Dallas before the start of the 2016-17 season.
"This is where I want to play; this is where I want to be," Benn said. "I don't think it's going to be a problem."
Benn finished third in the voting for the Hart Trophy this season after finishing second in the NHL with 89 points. He won the Art Ross Trophy as the League's leading scorer with 87 points in 2014-15.
Dallas re-signed Benn's brother, defenseman Jordie Benn, to a three-year contract Friday. Jordie Benn could have become an unrestricted free agent on July 1.
