Brees, 39, will become an unrestricted free agent on Wednesday. He and the Saints lost to Minnesota in the divisional playoff round this past season.
Brees has publicly vowed to remain a "Saint for life" and the team's preference is to pay him one year at a time. The Saints also would like to get a deal done quickly because if he remains unsigned Wednesday, $18 million in dead money from Brees' current contract immediately counts against the team's salary cap in 2018.
Brees signed a five-year contract extension with the Saints in 2016, although it included an automatic void after two years -- thus making him eligible for free agency this offseason.
It is expected that he will sign another short-term deal, along the lines of the one-year contract extension he signed in September 2016 that was worth $24.25 million.
Brees completed a career-high 72.0 percent of his passes for 4,334 yards and 23 touchdowns while leading the team to an 11-5 regular-season mark. The touchdown total, however, was his lowest since 2007.
The Vikings reached the NFC title game before losing to the Philadelphia Eagles with Case Keenum as their quarterback. Keenum is a free agent, and the Vikings are expected to be among the teams pursuing Kirk Cousins.