The NFL's franchise-tag deadline is March 5 with free agency set to begin a week after that.
Brees isn't surprised at the pace of the negotiations and said Thursday he's "still very optimistic" a long-term deal will be agreed to in the near future, according to The Times-Picayune. He added "this is definitely when things heat up."
"There's no doubt in my mind we'll get a deal done," Brees said.
Brees told NFL Network earlier this month that negotiations had started, and reiterated his confidence that a deal would likely be done before he officially becomes a free agent.
Brees disagreed the two sides are "very far apart" in philosophies on a new deal.
"I wouldn't say we're 'very far' apart. I think there's been progress made," he said. "But just like everything it's a process. It takes time. It's not something that happens overnight."