According to the Yorkshire Post, the Blues, along with Everton and Leeds, are ready to pounce if Brown's talks with Sheffield United fall through.
Any move for the former City midfielder would be good news as the Blues are set to cash-in from a sell-on clause which gives them a cut of any fee.
Meanwhile, Dutch defender Melchiot has dropped down the pecking order at Stamford Bridge after the signing of Glen Johnson from West Ham.
Manager, Claudio Ranieri, is reported to be ready to let the 26-year-old leave in January to allow another new face to come in at Chelsea.