Wilkerson will reunite with new Packers defensive coordinator Mike Pettine, who served in the same capacity with the New York Jets during the former's first two NFL seasons in 2011 and 2012.
Deals cannot be officially signed until the new league year begins on Wednesday at 4 p.m. ET.
The 28-year-old Wilkerson sat out the last three games of the 2017 season reportedly because he was late for a team meeting on Dec. 15. Multiple outlets reported that he was kept off the field because the Jets were concerned about potential injury, which could have resulted in New York being on the hook for his 2018 salary.
Wilkerson and the Jets were on much better terms in 2015, when he posted a career-high 12 sacks and was named to the Pro Bowl.
The Jets used the franchise tag on Wilkerson for 2016, but the sides worked out what became a five-year, $86 million extension before the July 15 deadline.
Wilkerson has recorded 404 tackles and 44.5 sacks in 105 career games since being selected by the Jets with the 30th overall pick of the 2011 NFL Draft.