The team announced it used the non-exclusive tag on the 25-year-old Monday.
The move was expected, as NFL Network Insider Ian Rapoport reported last month the Chiefs planned to use the tag, but still hoped to get a long-term deal in place with the stud DT.
Sides have until July 15 to work out a long-term deal.
The Chiefs were on both sides of the tag-and-trade last year, shipping Dee Ford to San Francisco, and acquiring and paying Frank Clark big money. Clark's contract could make a long-term deal for Jones tricky in K.C., so a potential trade can't be disregarded if a multi-year deal falls through.