Rivera says the trade is contingent on Beason passing a physical with the Giants.
The physical was scheduled for Friday morning, a person with knowledge of the situation told ESPN.com.
Beason was benched prior to Carolina's 38-0 Week 3 win over the Giants. With Rivera on Thursday, he broached the topic of wanting to play more.
"The trade benefits both the team and Jon," Rivera said. "We'll obviously get something out of it and it gives Jon an opportunity to get on the field."
Rivera wouldn't say what the Panthers will receive from the Giants in return for Beason.
Giants coach Tom Coughlin said Friday of the potential trade: "I don't have anything do add to what you already know."
Beason had microfracture surgery last October and looked slow in his first two starts. Chase Blackburn, a former Giant, replaced Beason in the lineup.
Friday's move initially was reported via Twitter by Fox Sports, which cited a Panthers source.
The Giants (0-4) rank 21st in the league in total defense and 28th against the rush.
Whether or not Beason can help remains a question. His play was a liability as Carolina (1-2) lost its first two games. In the opener, he missed a fourth-quarter tackle that resulted in the Seattle Seahawks getting out of a hole and running out the clock in a 12-7 win. A week later, in a 24-23 last-second road loss against the Buffalo Bills, Beason gave up five catches for 112 yards, including a 45-yarder to Stevie Johnson in which 35 yards came after the catch.
In his prime, Beason was one of the best in the league. He led the Panthers in tackles with 140 as a rookie in 2007 and was runner-up for the NFL Defensive Rookie of the Year Award.
He made his first Pro Bowl in his second season, recording 138 tackles and three interceptions. He continued at that pace until 2011, when his season ended early with the torn left Achilles tendon.
He has played in just seven games since.
This is the second time within a span of two years the Giants have dealt a late-round pick to acquire an injury-prone former first-round linebacker. The Giants sent a fifth-round pick to Cincinnati in 2012 for Keith Rivers, who has failed to be a difference-maker for the team. He played in just 11 games in 2012 and has eight tackles through the four games this season.
If healthy, Beason will have the chance to compete for quality minutes on a defense that lacks playmakers at linebacker. Mark Herzlich is the starting middle linebacker because of Dan Connor's season-ending injury, and backup Allen Bradford was claimed off waivers in September. Rivers has been ineffective. Spencer Paysinger has seemingly played the best of the unit.
If Beason passes the physical, the Giant will have two roster moves to make. Safety Will Hill is eligible to be activated after his four-game suspension for violating the NFL's substance abuse policy. Hill provides depth in the secondary and also contributes on special teams.
Offensive lineman Chris Snee (hip) said Friday he does not expect to play again this season and likely will undergo surgery, which could open a roster spot for Beason. Sources said earlier in the week the team was waiting to see if Snee would improve enough to be able play through the injury, as he did in 2012. The Giants have not yet made an official roster move.
Information from ESPN.com Panthers reporter David Newton, ESPNNewYork's Matt Ehalt and The Associated Press contributed to this article.