Mowbray is reported to have informed the former Hibernian ace that he was prepared to sell him during this month's transfer window.
Brown was remaining coy on talk that he could leave Celtic this month, but admitted he held talks with Mowbray about his future.
"Yes, there was a conversation between myself and the manager, but I am not prepared to go into details," Brown told the Daily Record.
"I believe these things should remain private. Maybe you should ask him what was said. I have nothing more to add."
The news is sure to fuel speculation that Brown could be on his way to England with the likes of Birmingham and Tottenham thought to be long-term admirers of the Scotland international.
Scottish Premier Winner 2009/10 Win Outright: Celtic 2/1