The Italian holding midfielder has allegedly not been approached by the Biancocelesti as he remains in the dark regarding his next destination in the upcoming transfer window
Italian sources claimed on Sunday that the Italian capital club were willing to offer the 34-year-old a two-year deal as he enters the final days of his Rossoneri contract.
"I have not yet received any offer from Lazio," Andrea D'Amico told Radio Mana Mana. "I have several offers, and Gattuso's desire to play is always the same. We must still find the right option.
"After he terminates his contract with Milan, we must meet to decide his future."
Gattuso announced earlier this month that he would leave the club in June, bringing an end to a 13-year spell with the Rossoneri.
He said that his priority was to return to Rangers, but such a possibility has been ruled out as the Scottish giants cannot sign players aged over 18 due to a transfer embargo.
Boca Juniors sporting director Pablo Budna has declared that the club are interested in the former Italy international, who missed most of the season because of a career-threatening eye problem.