FLOWERY BRANCH — Cornerback Brent Grimes knows the Atlanta defense must play a nearly perfect game to have a chance against New Orleans’ explosive offense.

“The odds are against us, obviously,” Grimes said Wednesday. “They’re the No. 1 offense, but we’ve got a chance to make a statement.”

Unfortunately for Grimes and his teammates, the Falcons (6-6) lead the NFL with 49 plays allowed of at least 20 yards. Opponents are converting 46 percent of third downs, second-most in the league.

Facing quarterback Drew Brees and the Saints (12-0) on Sunday seems to offer a worst-case scenario for a defense that’s managed just two interceptions over a seven-week stretch — during which Atlanta has lost five games.

It’s possible that Grimes, who had his only interception of the season six weeks ago at the Louisiana Superdome, could start at right cornerback if Chris Houston isn’t recovered from a strained hamstring.

The Falcons also don’t know the status of rookie cornerback Chris Owens, who started the last two games on the left side but was limited in practice Wednesday because of a tender shoulder.

Brees completed 25 of 33 passes for 308 yards, two touchdowns and one interception as the Saints beat Atlanta 35-27 in their first meeting. The nine-year veteran, now in his fourth season with New Orleans, leads the league with a 111.3 passer rating and 29 TDs.

“We turned it over four times the first time we played them,” Brees said. “We can’t do that again. There’s no doubt. I know we need to be prepared and ready to handle their pressure packages. They’ve been able to get after some teams and they’ve got some pretty good pressures that obviously we’re going to need to be ready for and have a plan for.”

The Falcons, however, have allowed 15 touchdowns in 22 red-zone drives over the last five weeks, not encouraging numbers for coach Mike Smith.

Equally troubling is Atlanta’s difficulty in not letting offenses get outside of its defensive containment.

“When you’re in the middle of the field, (the defense has) more players that can make the tackle,” said Smith, a former defensive coordinator with Jacksonville. “I would say percentage wise more plays on the perimeter go for longer yardage because there aren’t as many players out there.

John Abraham, a three-time Pro Bowl selection, has just 1.5 sacks since Week 1, and the Falcons have only 23 this season to tie Carolina for third-fewest in the NFC.

Smith insists the defense can correct its mistakes. He refuses to give opponents too much credit.

“Very rarely do you see a great throw and a great catch,” he said. “It’s usually either a mental error, a missed tackle or poor leverage. Those are the three things that contribute to an explosive play. It’s something we’ve been working all season long, trying to address, and something we haven’t gotten fixed.”

Defensive tackle Jonathan Babineaux believes Brees and his receiving corps of Marques Colston, Devery Henderson, Robert Meachem, tight end Jeremy Shockey and running backs Pierre Thomas and Reggie Bush will keep Atlanta moving from sideline to sideline.

New Orleans’ goal is to exhaust the Falcons long before the start of the fourth quarter.

“That’s how most people game-plan us coming into it,” Babineaux said. “We’ve done a good job stopping the run the last few weeks, and I think teams are noticing that and going outside the box to get the corners and safeties to tackle more. We’ve just got to be disciplined in everything we do and keep the ball in front of us.”