Safety Byrd is the Bills' most high-profile player to be out of contract during the off-season, and he spent this season playing under a franchise tag after talks stalled last summer.
Brandon is now keen to resume those talks, stating that keeping the Pro Bowl selection is a top priority.
He told the team's official website: "It's a process and there's no carryover. You start over again and you try to get something done. We just weren't able to come up with a solution that worked for both parties last year, so we'll reset it and start again.
"We all are hoping to get a deal done. And we're going to do the exact same thing this time, work our tails off to try to get another one done."
Last year's stalemate in talks saw Byrd delaying his decision to accept the contract until the final day of training camp in July.