The Bergen Record reports the deal for the unrestricted free agent will be for three years and worth approximately $3 million a season.
Zubrus, 35, has spent the past six seasons with the Devils. He had two goals and nine points in 22 games for New Jersey in 2012-13 after posting career-bests with 17 goals and 44 points while playing 82 games in '11-12.
Zubrus, who is 35 years old, told the Record's Tom Gulitti that the deal is not done yet, but he is hopeful it will be soon.
"As I said at the end of the [2012-13 season], my first choice is staying where I am," Zubrus told Gulitti. "That hasn't changed. I feel the same way. As of now, I'm still a Devil. My agent and Lou [Lamoriello] have talked. They're still talking and, hopefully, this is going to get done."
General manager Lou Lamoriello still has to try to sign unrestricted free agent forwards Patrik Elias and David Clarkson. Elias led the team in scoring with 36 points in 2012-13, and Clarkson was the Devils' top goal scorer with 15. Each player has spent his entire career with the Devils.