The West London club are long-term admirers of Murillo, 23, and are keen on adding him to their squad in the summer.
According to TeamTalk, Cheslea are planning a major defensive overhaul and are inviting offers for Adarabioyo, Badiashile, and Chalobah.
A deal to sign the Brazilian won’t be straight forward, however, with Liverpool also keen on signing him from struggling Forest.
Liverpool have already beaten Chelsea to the signing of Jeremy Jacquet, who will head to Anfield from Rennes in the summer for a reported £60 million.