Rossoneri director Silvano Ramaccioni announced yesterday that a deal was close, while the Italian press claimed the deal would be finalised today or at the latest 24 hours later.
However, Galliani revealed on Thursday night that the proposed loan deal had fallen through.
"Negotiations for Shevchenko are at the moment frozen," he told Gazzetta dello Sport.
"Milan had wanted to take the player on loan with the right to buy him, but Chelsea said no because they wanted us to buy him outright.
"Therefore negotiations are through."