"I'm told the Chiefs and Jones have begun talking, which is a big victory because it's been quiet for months on that front," Fowler told ESPN's "SportsCenter" on Saturday. "They've really had no communication. They've at least started negotiating.
"The Chiefs got the Patrick Mahomes deal done. They'd like to move on to Jones, who is considered a top-three defensive tackle, but that's going to cost them well over $20 million. It's just unclear how far they're willing to go at this point, but they want to keep one of their best players."
Jones, whom the Chiefs franchise tagged in March, tweeted in late June it's possible he "won't play" without a new deal.
The 26-year-old is among the NFL's premier interior defenders and played a significant role in Kansas City's Super Bowl campaign. He earned his first Pro Bowl nod in 2019 after notching nine sacks, though he set a career high with 15.5 the year prior.
Jones is set to make $16.1 million in 2020 if he signs the tag, according to Spotrac. He and the Chiefs have until July 15 to ink a multi-year deal or Jones must play under a one-year contract.