London duo Charlton and Millwall have been linked with the 22-year-old, whose contract at Ashton Gate expires at the end of the season.
"I'm not aware of any offers having been made for Danny Haynes and, as far as I know, there has been nothing official," Millen told the Bristol Evening Post.
"It's that time of year when the January transfer window is open and there are a lot of rumours going around. You have to take them with a pinch of salt."
Millen added: "Everyone knows our situation and that I'm trying to do some business in terms of moving players out in January. That is an ongoing process."
Source: PA
Source: PA