"We understand with the collective bargaining agreement that he has the ability to not be here right now, and we respect that. We really do," Marrone said Saturday.
The Bills, who designated Byrd as their franchise player in February, failed to reach a long-term agreement with the Pro Bowl safety by the July 15 deadline. Having not signed his one-year, $6.9 million tender, Byrd does not face any fines by not reporting to training camp.
"We respect him as a player and as a human being. Hopefully he comes in, and when he does, we'll welcome him with open arms," general manager Doug Whaley said. "But at this time, he's exercising his right, and we respect that."
Whaley on Saturday declined to comment on if there are any current talks between the two sides.
"Right now the lines of communication are open, but we will not be negotiating [in public]," he said. "I just think it's a normal negotiation process. We've worked hard, they've worked hard, and it's part of the business of football."
Once he reports, Byrd will have to adjust to a new defensive scheme under first-year defensive coordinator Mike Pettine.
"We try to give him a little bit of stuff so he doesn't come in and know nothing," cornerback Stephon Gilmore said Friday. "I think he'll be ready to go when he comes back."
"The type of person [Byrd] is, he'll be in shape and ready to go," Whaley added.
Byrd, 26, is the last of eight franchise-tagged players in the NFL not to sign his tender or agree to a long-term deal.