It generally starts browning or graying from the inside. This is because there's no oxygen getting through to the core, starting the myoglobin on it's pigment-creating journey. It's not uncommon to buy meat from the store, open it right up, and find brown on the inside. It's a totally normal process.
Again, "safe" here meaning that it's not rotten. If it has E. coli, it'll have E. Coli whether it's fresh or not.