The Portuguese Football Federation (FPF) axed Queiroz last week in the wake of his six-month ban for insulting anti-doping agents and are expected name his successor in the next few days.
Maradona, out of work since leaving his position as Argentina coach after the World Cup, fellow Argentine Jose Pekerman and former Mexico coach Jose Aguirre have been linked with the position.
Former Sporting coach Paulo Bento is seen by the local media as the strongest candidate but according to other reports, some FPF directors believe Portugal need an overseas coach with an international pedigree who is used to dealing with global stars such as Cristiano Ronaldo, who failed to shine under Queiroz.
Portugal's Euro 2012 qualifying hopes have been hit by a dismal start. A 4-4 draw at home to Cyprus was followed by a 1-0 defeat in Norway.
"It's true (Maradona is interested). Diego and I talked about it and it is a project that attracts us. He is willing and has availability, but has not been contacted yet," Alejandro Mancuso, one of Maradona's assistants during his spell as Argentina coach, told the A Bola sports daily.
Pekerman, another former Argentina coach, is also interested in the Portugal job, according to his agent.
"Many national sides wanted to hire him, but he was not interested. The Portuguese team, yes, that interests him," agent Jose Sanchez Parra told Portuguese radio Renascenca.
He added that Aguirre, who resigned as Mexico coach in June, has also shown an interest in the position.
Prior to Queiroz, Portugal also had a coach from Latin America. Brazil's Luiz Felipe Scolari took the team to the final of Euro 2004 and the semi-finals of the 2006 World Cup.
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