In October, the Portuguese said that hotel living was "a bit of a disaster", and United struggled for form until a recent improvement in results.
"I know that if one day they bring a new contract, I will sign it," he said.
Mourinho says he will not be making the switch to China - although he admitted that "China money is attractive for everyone".
"I want to stay in the most difficult place to win," he said.
"Too young, too many years of football to go to a place like China. China money is attractive for everyone but I love more my football at the highest level."