Per ESPN's Adam Schefter, the two sides are "extremely close to a lucrative new extension that the two sides are hoping to finalize in the next few days."
Schefter added the Saints and Kamara have a window to get the deal done with players having an off day Tuesday.
Last week, there were conflicting reports about Kamara's absence from Saints practice.
Schefter reported Kamara had three unexcused absences from practice that were believed to be related to his contract. NFL Network's Tom Pelissero noted the 25-year-old received an epidural shot in his back.
Speaking to reporters Monday, Kamara denied that he was away from the team because of a contract holdout: "Not really, I ain't ever held out in my life. That's about it."
Amid the ongoing debate about running back value in the NFL, teams have shown a willingness to invest in star players at the position this offseason. Christian McCaffrey signed a four-year extension with the Carolina Panthers worth up to $64 million.
The Cincinnati Bengals gave Joe Mixon a four-year, $48 million extension last week.
Kamara is entering the final year of his rookie contract. His $2.13 million base salary is tied for 18th among all running backs in 2020, per Spotrac.
A third-round draft pick out of Tennessee in 2017, Kamara has averaged 1,492 yards from scrimmage and 12 total touchdowns in three seasons with the Saints. He's led the team in rushing yards the past two seasons.