The Brazilian side confirmed that they were close to signing 35-year-old on Tuesday, but his decision to delay a meeting with the club's officials has seen the move collapse.
Mineiro's director of football Eduardo Maluf revealed in a statement: "We said that yesterday was the deadline for an agreement or explanation, as we would like to have him on board for our Libertadores bid. Today, however, we received an email from Mr Casini, saying that Anelka, a Muslim, was in Kuwait for an event and would only come on the April 19.
"He had the obligation of informing us about this, but we only heard about it know. I talked to our president and we agreed that Atletico's greatness is much bigger than a single player and, therefore we are cancelling our commitment."
Anelka was sacked by the Baggies in March shortly after being handed a five-match ban for using the controversial 'quenelle' gesture during a goal celebration.