Bryant's contract, which calls for a $12.5 million base salary next season and account for a $16.5 million cap charge, is the source of consternation for Dallas, which wants to restructure the deal.
Jones did not want to address specifics of the contracts while speaking with reporters at the NFL Combine in Indianapolis, but he left no doubt that the Cowboys want Bryant on the roster.
"As we sit right here, yes," Jones said, per the Dallas Morning News. "It takes two to do anything with his contract."
Bryant had a team-leading 69 receptions for 838 yards and six touchdowns in 2017. He has gone a career-worst 23 regular-season games without a 100-yard performance.
The three-time Pro Bowl selection has failed to record a 1,000-yard season or reel in more than eight touchdown receptions in a campaign since signing a five-year, $70 million deal in 2015.
Bryant told a Dallas radio station last month that he could not picture himself playing for another team.
However, Cowboys executive vice president Stephen Jones said that Bryant's emotional personality on and off the field can be a "distraction" to the team.