"We have been in contact with Julio and his representation," general manager Thomas Dimitroff said in a statement. "We will not discuss those conversations publicly except to say we feel they have been productive and constructive. We understand the concerns and thoughts from their perspective. Although not ideal, Julio informed us today he would not be attending minicamp.
"We have much respect for him and what he means to our team, our city and our fans."
The 29-year-old Jones, who missed the voluntary organized team activities, wants a new contract, as previously reported by NFL Network Insider Ian Rapoport.
Atlanta recently took care of quarterback Matt Ryan with a contract extension, but it remains to be seen what the team will do with Jones. The star wide receiver has three years remaining on his current deal and will earn a base salary of $10.5 million in 2018.
While Jones was not subject to fines for missing OTAs, he now places himself in position to face monetary penalties for missing the mandatory portion of the offseason workout program.