Galliani says Tevez is willing to take a major pay-cut to make the move.
"Between yesterday and today I laid a few bricks to reinforce an already formidable squad," he told Milan Channel.
"I've been in my office with Tevez's agent and the situation is clear. Milan have an agreement with the player and just now we sent a proposal to Manchester City: a free loan with right to buy at certain conditions.
"Why should City accept that? He is not playing, he's a great player and if he does well with us then we'll buy him.
"The player is giving up a mountain of money. He had enormous bonuses with City for the Premiership and Champions League.
"I spoke to Carlitos and he wants to join us. Half the agreement is complete, now we await City's response.
"If Tevez arrives, it'd be a new champion for all of Italian football to enjoy. We are close, the player was fantastic for the economic sacrifices he made and his great desire to come to Milan.
"I hope City say yes, as I managed to beat away some threats from Italy and Europe, but I cannot tell you who... We are in Pole Position."