"That part of it is still the same," Brown told The Cincinnati Enquirer at the NFL Annual Meeting in New Orleans. "I didn't say anything inconsistent with that. I want him back, and I will just leave it at that. I haven't talked to any other team about him, and I have no plans to trade him."
Brown said the same to Palmer following his original demand, but sources close to the quarterback suggest he could retire if he's not traded, according to The Enquirer.
"I've seen any number of players who at one point did not want to reenlist come back and come back and be quite happy about it," Brown said Monday. "It depends how it goes. As far as getting value, I don't see any opportunity to get what I consider to be value. Having said that, it doesn't make sense to look to trade. It only makes sense to wait and hope Carson comes around."
Brown acknowledged that the Bengals needed to enter next season with answers -- not mystery -- at quarterback, and they could address the position in April's draft, or take a closer look at backups Jordan Palmer or Dan LeFevour.
"The quarterback position is one that is key, and we don't know how that is going to end up," Brown said. "That's a very big question still to be answered. If it is answered right, our chances will be pretty good. We're going to try to get it answered right, and there are different ways to do that."
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, but the quarterback has few options if the Bengals decide they want to keep him.
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 during the 2009 season. The offense has been in flux, bouncing from a run-based approach in 2009 to a mix of run-and-pass that didn't work in 2010, leading to coordinator Bob Bratkowski's ouster and Jay Gruden's hiring this offseason.
With Terrell Owens and Chad Ochocinco as his top targets, Palmer completed 362 of a team-record 586 attempts for 3,970 yards and 26 touchdowns last season. He also matched his career high with 20 interceptions.
The Associated Press contributed to this report.