Saints coach Sean Payton told ESPN recently that the team would consider drafting a quarterback in the first round. With Mitchel Trubisky, Deshaun Watson, and Patrick Mahomes off of the board, that leaves Notre Dame's DeShone Kizer and Cal's Davis Webb as the top passing prospects. Pittsburgh's Nathan Peterman and Miami's Brad Kaaya are also available, but could slip to the final day of the draft.
Brees, 38, is playing on the final year of a two-year, $44.25 million contract. He'll make $13 million in 2017.
Rodgers, 33, is signed through 2019. The two-time NFL MVP led the NFL last season with 40 touchdown passes.
NFL Network reported Friday that the Packers are getting trade calls but the franchise might keep its No. 33 selection Friday and take Kizer.
Rodgers is due $12.55 million, with $600,000 in per-game roster bonuses this season for the Packers.
Last month, Brees told Sirius XM NFL Radio that he thinks he can play until he's 45-years-old.
Payton says that the Saints are "in the quarterback business always."
"I think that topic exists and has existed because of the nature of the position," Payton told Bruce Murray and Brady Quinn on the SiriusXM Blitz. "I think we're in the quarterback business always because they're so difficult to find. And there's been a year or two we're close to drafting maybe a player (at the position) and he went a little before we were ready to pick. And certainly you pay attention to it when your quarterback's older."
In January, Brees told the New Orleans Times-Picayune that he plans to play out the season without an extension.
Brees has led the NFL in passing yards in five of the last six seasons. Last year, he completed 70 percent of his passes for 5,208 yards, 37 touchdowns, and 15 interceptions. He has nine consecutive seasons with at least 32 touchdown passes. Last season, he also threw a league-most and career-high 673 passes. The 10-time Pro Bowl selection and former All-Pro has passed for 465 career touchdowns, the third-most in NFL history. His 283.7 passing yards per game are the most all time.
The Saints drafted Ohio State cornerback Marshon Lattimore with the No. 11 overall pick Thursday while the Packers traded its first-round selection to the Cleveland Browns. The Browns picked Miami tight end David Njoku with the No. 29 overall selection.