"It's awfully close. I hope he'll be out at [minicamp] tomorrow," Jones said on Monday, via Jon Machota of the Dallas Morning News.
NFL Network Insider Ian Rapoport reported Monday that it will be a six-year deal that will provide Martin with the largest guaranteed payout at his position in NFL history.
A four-time Pro Bowl selection, Martin has missed the team's voluntary offseason work as he seeks a contract extension.
Martin is set to play this season on the fifth-year option of his rookie contract. The 6-foot-4, 315-pound Martin will earn a base salary of $9.3 million in 2018.
A first-round draft pick (No. 16 overall) in 2014, Martin has started all 16 games in each of his four seasons, earning first-team All-Pro honors both as a rookie and in 2016.