Beckham is set to join AC Milan on a short term loan deal from January to March.
Galliani told Tuttosport: “At first we though they [Beckham’s lawyers] would be in Milan next week but instead they arrived today.
“We will begin negotiations but I don’t know if it will conclude in a positive way or not but I am hoping we can conclude it in the best manner.
“There is still someway to go as we have to finalise everything.”
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.