The defender flew in to Italy on Friday accompanied by FIFA agent Ernesto Bronzetti and had dinner with Rossoneri Vice-President Adriano Galliani.
Sky Sport Italia report Rami underwent a medical today and passed with flying colours, as he is 1kg below his ideal weight.
However, Valencia sources pointed out the deal on loan with option to buy for €7m was not completed yet.
Rami is expected to fly back to Spain tomorrow. When the move does go through, he will only be eligible to play for Milan from January.