Jones has been working out in Florida with a trainer since he left the Packers' offseason program about a month ago.
The source said Jones, who was the 61st overall pick in the 2017 draft, believes it would be best for both him and the Packers if they parted ways.
Jones has been in and out of the lineup during his two years in Green Bay, starting 12 games over two years. The Packers opened last season with former undrafted rookie Kentrell Brice and Ha Ha Clinton-Dix at safety. Even after Clinton-Dix was traded midway through last season, Jones was bypassed for a starting job when the Packers moved Tramon Williams from cornerback to safety. It wasn't until after Brice sustained an ankle injury in Week 10 that Jones finally got his first start of the season in Week 11.
Jones had originally reported to the Packers for the start of offseason workouts on April 8. The Packers made a significant commitment to the safety position in the offseason when they signed former Chicago Bears safety Adrian Amos to a four-year, $36 million contract in free agency and then used the 21st overall pick in the draft on Maryland safety Darnell Savage Jr.
Packers coach Matt LaFleur said Tuesday that he has not spoken with Jones since he left the offseason program shortly after the draft, but said general manager Brian Gutekunst has been the point man in the Jones situation.
"Honestly, that's something that I'm going to let Gutey handle, and we'll go from there," LaFleur said.
Jones can't be fined for skipping these voluntary workouts, but he could be if he skips the mandatory minicamp from June 11-13.
"Right now, I'm just going to focus on the guys that are here," LaFleur said. "I guess we'll cross that bridge when it comes. But that's something that I know Gutey has a good handle on that situation."
As a rookie, Jones played in all 16 games with seven starts. He was one of just three Packers rookies to appear in every game during the 2017 season. He posted 71 tackles with two sacks plus an interception and seven pass breakups. In his first career start (Week 3 of 2017 against the Bengals), Jones posted a career-high 11 tackles (10 solo) and became the first rookie defensive back in team history to record two sacks in a game.