"I would like Aragones to be the new national coach because he is very experienced, but my conviction is that national teams should be coached by men from the country itself," the Portuguese manager told a news conference.
"I don't like to see Portugal lose or draw games. I hope things change. They have good enough players to turn the situation around," he added.
Aragones, 72, coached Spain between 2004 and 2008. He is credited with laying the foundations for Spain's World Cup win this year by guiding the team to the Euro 2008 title with the introduction of a short-passing style.
"I am keen to coach in any place. I would go to any national team or club outside of Spain. I want to continue working," Aragones told Spanish radio station Cadena COPE on Tuesday.
Portugal's football federation on Thursday sacked Queiroz after a disciplinary feud sparked by a six-month ban for insulting officials from the country's anti-doping body.
The former Manchester United boss, who took over in July 2008, also paid a heavy price for a loss of form that saw his team struggle to reach the World Cup and pick up just a point from their opening two Euro 2012 qualifiers.
Humberto Coelho, who guided the national side to the semi-finals at Euro 2000, is another name cited by the press.
Portugal are second from bottom of Group H in their Euro 2012 qualifying table with one point from their first two qualifiers having lost 1-0 in Norway on Tuesday following a 4-4 draw at home to Cyprus last week.
Source: AFP Global Edition