The Portuguese Football Federation (FPF) have earmarked Mourinho as the man they want to lead the national team for the Euro 2012 qualifiers against Denmark on October 8 and Iceland four days later while they go about appointing a full-time successor to Carlos Queiroz.
But in a press conference on Friday, he said: "If it were not for Real Madrid I would do it for free.
"But if you ask me right now if I can go, I think not. I have a contract with Real Madrid. I do not say no, but in the natural way of things, I do not think this is the time."
Queiroz was sacked last week after being handed a six-month suspension for insulting anti-doping agents prior to the World Cup.
It has left Portugal in a difficult position, especially as they have taken just one point from their opening two Euro 2012 qualifiers with two more matches coming up next month.
The situation has left Mourinho, who only took charge at the Bernabeu at the end of last season, torn. Real Madrid have every right in the world to put an obstacle in the way," he said. "And if you put the slightest obstacle there, I can't go.
"To say no to Portugal is impossible because of my personal pride and my passion for Portugal, but at the moment I cannot say yes."