The Portuguese Football Federation (FPF) have approached the two-time Champions League winner to see if he would take charge for the games at home to Denmark on October 8 and away to Iceland four days later.
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"I don't understand why Real will not let me coach Portugal when I will have almost nothing to do in Madrid," Mourinho told Portuguese television, in quotes picked up by the Spanish media, after their 2-1 La Liga victory at Real Sociedad on Saturday.
"I will have nine days holiday in Madrid while there are international matches."
Real's director general Jorge Valdano moved quickly to clarify the club's position.
"There has not been an official request from Portugal so we have not declared our position," he told reporters.
"It has been a huge story in the media so the president of the Portuguese federation rang (Real president) Florentino Perez, but this was to say they had dropped the idea.
"We gave this to mean the issue was over. Mourinho is put out because everyone would like to help their country and this reflects well on him, but there isn't anyone to blame at the club."
Mourinho had told a news conference at Real's training ground on Friday he was unable to accept the offer as he believed his club would not have reacted positively to his absence.
Portugal sacked Carlos Queiroz this month after he was suspended for six months for insulting anti-doping agents before the World Cup and have yet to name a replacement.
They have had a poor start to their qualifying campaign, with a 4-4 home draw against Cyprus.
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