The holding midfielder's representative has revealed that the ambitious and big-spending Russian side have not given up hopes of signing the World Cup winner just yet
Anzhi already showed an interest in signing the 2006 World Cup winner during the summer transfer window, but Gattuso opted to stay at San Siro instead.
Nevertheless, the Russian club have refused to give up hope of luring the 33-year-old to Dagestan just yet.
"Anzhi were interested in signing him before and they still want him. There are no new developments at the moment though," D'Amico was quoted as saying by Sportitalia.
"We will talk with Milan and see what happens. He's been an AC Milan player for quite a while now and we have always been able to agree terms. We will soon talk to [Adriano] Galliani and find out what his plans are."
Gattuso's contract with the Serie A champions expires at the end of the 2011-12 season.