The 36-year old midfielder has been released after almost two decades with the Rossoneri with his representative Moreno Roggi revealing that they turned down an approach from MLS champions LA Galaxy in order to speak with the Hammers.
"Massimo did expect this decision but he was still a bit upset (to leave Milan). At this moment, seeing as he feels in good shape physically, we will evaluate offers," he told Radioblu.
"The situation is we turned down an offer from LA Galaxy. We have negotiations going on with West Ham but nothing with Fiorentina, as they have not made us any proposals. Having said that, I do hear Ambrosini is on the list for the Viola if David Pizarro leaves.
"We received another offer [on Wednesday] morning from Australia."