Palmer, who has four years left on his contract, told one of the NFL's least-successful franchises in January that he would retire if he's not traded.
The Bengals have had two winning seasons in the last 20 years, one of the worst stretches of futility in league history.
Bengals front office sources told Holtzman it is possible Palmer could report to the Bengals next week. The 31-year-old Palmer has never filed retirement papers, so the team would be obligated to pay him or trade him.
Brown has said the team will not trade Palmer, who is scheduled to make $11.5 million this season if he plays.
A source close to Palmer told ESPN NFL Insider Adam Schefter said nothing has changed in terms of Palmer's situation.
Last week the Bengals waived Palmer's younger brother Jordan Palmer, giving older brother Carson more reason to stay away.
Jordan was the No. 2 quarterback last season behind his brother, and was signed to another contract at the start of training camp, hoping to get a chance to compete for a job. But it became clear quickly that Cincinnati had other plans.
Information from the Associated Press was used in this report.