"He was told that, and that we count on him going forward," Brown told The Cincinnati Enquirer and the team's website Monday. "He was told that we are not in a position to trade him."
The franchise quarterback evidently decided it's time to leave his mess of a team.
Palmer hasn't talked to the media since making his trade request. A text message seeking comment wasn't returned.
Palmer's agent, David Dunn, issued a statement Monday about the meeting between his client and Brown:
"Carson met with Bengals owner Mike Brown recently. They both expressed profound disappointment in how the team fared last season, and in how it has generally performed during Carson's tenure with the team. Because of the lack of success that Carson and the Bengals have experienced together, Carson strongly feels that a separation between him and the Bengals would be in the best interest of both parties. Carson could not respect the Brown family any more than he does or be more appreciative of what the Browns have done for him and his wife Shaelyn and his family."
Palmer was the franchise's building block when it made him the first overall draft pick in 2003, Marvin Lewis' first season as coach. Palmer led the Bengals to the playoffs in 2005 and 2009 -- their only winning records in the last 20 years -- and rebounded from severe knee and elbow injuries along the way.
Palmer's trade request is another telling moment for a franchise coming off a 4-12 season that was in many ways the most disappointing in its history. Lewis decided to stay even though Brown refused to make any significant changes in how the team operates. Brown, Lewis and the staff are in Alabama this week to coach players for the Senior Bowl.
During the taping of an episode of "The T.Ocho Show" that will air Tuesday night on the Versus cable network, wide receivers Chad Ochocinco and Terrell Owens said Palmer was unhappy with Lewis and the front office.
"If he's asking for a trade, he obviously wasn't comfortable with the rehiring of Marvin Lewis," said Owens, who is a free agent. "He's been very stealth and discreet with his message, but he's saying there's a problem without saying there's a problem."
"At this point, I think he's frustrated with management and the head coach, management not embracing him ... a bunch of stuff," said Ochocinco, whose contract in Cincinnati runs through 2011.
Palmer's request is an indication he doesn't believe the team can win the way it currently operates. Brown said they didn't get into specifics of what was bothering Palmer.
"We'll just have to see how it plays out," Brown said. "We'll reach out to him and understand the things that are in his craw. Maybe there are things we can do that will appeal to him. We'll try to and see whether he can get it fit back together in the future."
Brown has a history of refusing players' requests for trades. When Ochocinco asked to be traded before the 2008 season, Brown dug in. Ochocinco expects the same to happen with his quarterback.
On Monday, Ochocinco tweeted: "no everything is not messed up in Cincy, we will be fine, Carson isn't going anywhere ... relax."
Palmer has few options if the team decides it wants to keep him. The question is how having an unhappy quarterback will affect the organization.
Late in the 2005 season, Palmer agreed to rework his contract to give the Bengals more salary-cap flexibility. He had six years added to the deal, which lasts through 2014. At the time, he said he wanted to finish his career in Cincinnati.
Since then, the Bengals have made the playoffs only one more time, losing to the New York Jets in the 2009 season. The offense has been in flux, bouncing from a run-based approach in 2009 to a mix of run-and-pass last season that didn't work. With Owens and Ochocinco as his top targets, Palmer completed 362 of a team-record 586 attempts for 3,970 yards and 26 touchdowns. He also matched his career high with 20 interceptions.
Owens is a free agent unlikely to return. As the season went along, he openly questioned the coaches' play-calling, saying the Bengals should throw more. Running back Cedric Benson, another free agent, said the team should have stayed with its run-first philosophy.
Brown believes they still can coexist.
"The life of a pro quarterback is not always easy," Brown said. "When you're down, the criticism will flare up. That's the nature of our business. We him to re-up, be in good spirits, and in time, he'll come around. This was a deeply disappointing season for us, we have all suffered from it. I think we will rebound."
The Associated Press contributed to this report.