"He's going to gut this place," Jackson told CSN Bay Area.
"He (McKenzie) wants to bring in his own guys," Jackson added. "No job is safe right now."
The Raiders went 8-8 in Jackson's lone season as coach, a season defined by his decision to trade multiple draft picks to the Cincinnati Bengals for quarterback Carson Palmer after Jason Campbell went down with a broken collarbone.
After starting the season 7-4, the Raiders lost four of their final five games to mark their ninth straight season without a winning record or a playoff berth. A late-game collapse at home to Detroit and a 38-26 loss to San Diego at home in the season finale did in the Raiders and ultimately Jackson.
The Raiders opted to reorganize their football operations department following the death of owner Al Davis on Oct. 8 death at age 82. Davis made all football-related decisions, from hiring coaches and other staff to having final say on draft picks and free agency.
Owner Mark Davis, Al's son, made the decision to bring in McKenzie last week and gave him the authority over the coaching staff. McKenzie, previously the Green Bay Packers' director of football operations, will now get to pick a new head coach to provide the Raiders a fresh start in their first full season without Al Davis involved since 1962.
The Raiders had already scheduled a news conference for Tuesday at 5 p.m. ET to introduce McKenzie.
Oakland had gone without someone in a true GM role since Davis' longtime senior assistant, Bruce Allen, departed for the Tampa Bay Buccaneers after the 2003 season. Allen had been a top personnel executive for Davis from 1996-2003. Prior to McKenzie's hiring, Davis' son, Mark, was making many top decisions.
Numerous league sources told NFL Network insider Jason La Canfora that they expect Packers assistant coach Winston Moss to be a leading candidate to replace Jackson.
A league source told NFL.com's Steve Wyche that Packers secondary coach Darren Perry likely would be hired as the defensive coordinator if Moss is hired, as expected.
The Associated Press contributed to this report