The two sides have until July 15 to strike an agreement. Otherwise, Jones will be limited to playing on the one-year tender in 2020.
When they tagged their star defender, the Chiefs reportedly had plans to work out a multi-year contract with him. However, Kansas City is short on cap space and needs to budget for a massive extension for quarterback Patrick Mahomes.
Jones, who'll turn 26 in July, notched nine sacks in 13 games last year. He had 15.5 sacks in a breakout 2018 campaign.