Matthews, 26, is the highest-ranked 3-4 outside linebacker in the league, according to ProFootballFocus.com, with at least 40 sacks, 20 stuffs and 20 passes defended.
Matthews, who came into the NFL in 2009, has 42.5 sacks, with 13 of those coming last season. He also has 204 tackles, seven forced fumbles and four interceptions since being the Packers' top draft pick in 2009 (26th overall).
The length of Matthews' new contract and the overall amount have not been disclosed.
The Packers are also working on a new long-term deal with quarterback Aaron Rodgers, who is seeking a multi-year deal of $25 million per year, which would make him the highest-paid player in NFL history.
The ESPN.com report said both Matthews and Rodgers may skip the start of the Packers' offseason workout program that begins April 15 unless a deal is in place by then. That possibility could occur in both players' cases.
In an interview Tuesday with Milwaukee radio station 102.9 FM, Rodgers said, "We'll see what happens here. I don't have an answer for you."
Rodgers' current contract, a six-year, $65 million deal he signed in 2008, expires following the 2014 season. The final year of that deal is reportedly worth $10.5 million.