Mourinho was quoted as saying: "Tell the FA to come and get me," in one national newspaper on Wednesday morning.
But the former Chelsea boss was more circumspect when speaking outside his home later in the evening.
"I know nothing, I know nothing about it," he told Sky News. "The only thing I know is I should be on my sofa watching the game and you knock on my door. I have nothing to say."
Asked if he would want the job, Mourinho added: "I cannot answer you. My job at the moment is to take care of my family, things in Portugal, enjoy my life - not 100% because no football - but enjoying my life.
"There are lots of good managers around the world.
"The only thing I say it's a pity England is not in Euro 2008 but for sure they will be back for the World Cup in South Africa, they have to choose the right person for that."