Brady's only win against Brees came just over 14 years ago when he was a senior at Michigan and Brees was in his junior year at Purdue.
Brees has since topped Brady and the Patriots twice with San Diego and once in New Orleans. Brady, though, is focused more on executing the basics with his struggling offense, which could feature tight end Rob Gronkowski for the first time this season.
Gronkowski has been recovering from offseason surgeries on his broken left forearm and back. He participated in practice on a limited basis Wednesday, and there has been little indication as to when he will return.
"Our job is to go out there and score, so we're not doing a great job of that," Brady said. "Our execution has to be a lot better, and that's what we're working on. We're trying to improve in all areas. It's frustrating when we don't score, but we're going to try to do better this weekend."
A year after leading the league in scoring and yards per game, the Patriots (4-1) are 24th in points (19.0) and 18th in yards (343.4) after last Sunday's 13-6 loss at Cincinnati.
It was Brady's first regular-season game without a touchdown pass since Jan. 3, 2010, against Houston.
Five games before that, he played Brees and the Saints in New Orleans and also failed to pass for a TD in a 38-17 loss Nov. 30, 2009. Brees threw five touchdown passes in that meeting, the last between the teams.
While Brady has been without Gronkowski, Brees and tight end Jimmy Graham are more in tune than ever for the Saints (5-0).
Graham leads the league with 593 receiving yards and is tied for second with 37 catches and six touchdowns.
"I'm just blessed to be with such a great quarterback and a guy who has so much trust in me," Graham said.
It's something Patriots coach Bill Belichick sees as a part of an offense that makes teams defend the whole field.
"I think they're definitely a hard team to prepare for," Belichick said. "... They attack the width of the field and they certainly attack the depth of the field. They run vertical routes. They run deep seem routes. They run check-downs and screens and those types of patterns, too.
"So you've got to defend from sideline to sideline. You've got to defend from the line of scrimmage really pretty much to the back end line. That's a lot of space defensively to account for, but that's basically their attack."
Defending is what the Patriots have done well this year with the second-best scoring defense in the league at 14.0 points per game.
The Saints aren't far behind in fourth (14.6), which might have something to do with their offense holding onto the ball. Their average time of possession is a league-best 34 minutes, 37 seconds.
"You want to score every time you have it, so we're not purposely trying to create long drives," coach Sean Payton said. "But be efficient with your plays, and if you're winning on third down, for instance, you're staying on the field. If you're turning the ball over, conversely, all of a sudden the drive ends. There's a lot of things that factor into it."
They had the ball for 36:00 in last Sunday's 26-18 win in Chicago, where Brees went 29 of 35 for 288 yards and two touchdowns while not throwing an interception for the second straight game.
The Saints have given the ball away an NFC-low five times and have a plus-6 turnover differential.
The Patriots have given it away just six times with a plus-4 differential, but their drives are stalling.
Brady's passer rating of 80.5 and completion percentage of 56.6 are his lowest since taking over the starting job in 2001.
"I think we'll try to put together any drive at this point to score points," Brady said. "Long, short - it doesn't matter. We've got to score touchdowns."