Seattle could announce as early as Monday afternoon that Bennett will remain with the Super Bowl champions, according to the sources.
The Chicago Bears reportedly have been heavily pursuing Bennett, one of the top available defensive free agents.
Bennett was Seattle's best defensive lineman in 2013 after signing a one-year deal worth $4.8 million. He played his first four seasons with Tampa Bay after the Seahawks released him as an undrafted rookie in 2009.
The 6-foot-4 Bennett was everything and more the Seahawks hoped he'd be when they brought him back for the 2013 season. He had 8.5 sacks in the regular season along with one forced fumble and one fumble recovery, which he returned 22 yards for a touchdown.
Bennett's versatility and quickness were major assets for Seattle, and he played both end and tackle.
He had six tackles, a forced fumble, a fumble recovery and a half-sack in the Seahawks' divisional-round playoff game against New Orleans. He kept it up in the NFC Championship Game, posting a sack and recovering a fumble that he returned 17 yards to the San Francisco 49ers' 6-yard-line.
ESPN.com Seahawks reporter Terry Blount contributed to this report.