The French centre-back has been on the Italian club's radar this summer following the departure of Alessandro Nesta and Thiago Silva.
However, Galliani has now admitted defeat in their pursuit of the 23-year-old.
"Montpellier turned down our offer and we cannot reach an agreement for buying the player," he said.
"Therefore, the case is closed with no regrets or bitterness. We have already identified other targets, but I won't tell you who they are even under torture!"
Yanga-Mbiwa's current contract with Montpellier runs out in June 2013.