Burke, 32, has called out of favour at Forest under Dougie Freedman, playing just one of the last 13 games.
He went six games without even being included in the matchday squad, and has not been named in either of the last two squads.
The Scottish international is clearly not fancied by Forest anymore, and Rotherham boss Neil Redfearn is ready to push through a move to sign the winger this month.
Luciano Becchio has already been added to Rotherham’s squad, and Redfearn wants the winger in to provide a threat from wide and create chances for the striker.
Forest are ready to sanction his departure this month, with just six months left on Burke’s contract. They would rather sell him now for a small profit than lose him for free in the summer.
It is not indicated in the report that Rotherham have yet submitted a bid for Burke, but Redfearn is sure to make a formal approach for one of his prime targets in the coming days.