The first area of concern for the Portuguese was revealed to be left back, where an alternative to Marcelo is being sought, and right back, a position vacated by the switch to central defence of Sergio Ramos planned by Mourinho.
Mourinho wants a more defensive player on the left side and, while Cole has many attacking talents, he is recognised as a far more assured defender than the Brazilian.
The former Chelsea manager said: "I also would like to have an alternative left-back to Marcelo. Marcelo has his characteristics but Real needs a balanced squad, different players for each position. I would like a left-back that has different characteristics to Marcelo."