At the time of writing this (16 January 2013) Jose Mourinho is still in his job, but things are happening fast and it could still happen. He has always had a difficult relationship with his employers; he was sacked from Chelsea in 2007 and the reason often given for that is that he always wants total control of the team and will not listen to others' opinions - which didn't suit Chelsea boss Roman Abramovitch.
Now he is having similar problems in Real Madrid. Florentino Perez is also said not to be happy with Mourinho's leadership style, and a lot of his decisions have been questioned lately, such as dropping Iker Casillas from the team. However, Perez has not made any public statement that he is getting rid of Mourinho.
It is also possible that the manager may leave of his own accord - lately he has been saying he would like to work in England again. He hasn't been offered his old job back yet, but he and Abromovitch have healed their old rift, so it's not impossible.