The Saints were unable to agree to a long-term deal with Brees and didn't want to risk losing him in free agency.
The franchise tag for a quarterback currently carries a $14.4 million salary cap hit, but the number could increase later this spring when the quarterback cap numbers are re-evaluated.
Sources told ESPN NFL Insider Adam Schefter on Friday that Brees and the Saints remain millions of dollars apart in contract talks.
The two sides, both of which believe they are making a fair offer, are facing a gap of $5 million per season for the first three seasons of the proposal, sources told Schefter.
Brees is seeking a contract that averages $23 million per season for the first three years of his deal, sources told Schefter.
That's the same amount Peyton Manning's Colts contract averages the first three seasons.
But the Saints are offering Brees a five-year contract that averages $18 million a year, sources told Schefter, which is the average that Manning and New England's Tom Brady are due to earn over the life of their deals.
Brady's contract averages $18 million in the first three years, like the Saints' current offer to Brees.
In January, Brees said he would be "beyond stunned" if he and the Saints are unable to agree on a contract extension during this offseason.
The 2011 Offensive Player of the Year arrived in New Orleans in 2006, less than a year after Hurricane Katrina had struck. Since then he has passed for more yards than any other quarterback in the NFL (28,394) while lifting the Saints to new heights and simultaneously helping a region heal from Katrina's devastation.
In 2011, Brees set NFL single-season records with 468 completions, 5,476 yards passing and a completion percentage of 71.2. His prolific passing numbers helped the Saints set a new NFL high for total offensive yards in a season with 7,474.
The 33-year-old Brees led the Saints to a 13-3 regular season record and second NFC South division title. New Orleans defeated Detroit in the first round of the playoffs before falling in the final seconds of their second-round game at San Francisco.
Under the rules of the exclusive franchise tag, Brees can't be contacted by other teams and remains exclusive property of the Saints.
John Clayton is a senior NFL writer for ESPN.com. Information from The Associated Press was used in this report.