The 49-year-old has been out of work since leaving Galatasaray at the end of last season.
Mancini had been linked with taking over from Cesare Prandelli as Italy national coach following their first-round World Cup exit, but Antonio Conte got the nod instead after winning his third straight Scudetto with Juventus.
After Portugal's shock 1-0 loss to Albania in their opening Euro 2016 qualifier last Sunday, head coach Paulo Bento departed and Mancini would like to succeed him.
"I am still a young coach with a long career in front of me and a lot to learn," he told Portuguese newspaper Record.
"I like to experience different adventures. I've already worked in England and Turkey, while returning to Italy is an option, but I prefer to try new things.
"Would I go to Portugal? Of course. You know more than me that Portugal has always boasted high quality football full of class and talent, producing some of the best players in the world. The Portuguese clubs have also impressed in Europe.
"Would I be the Portugal coach? It would be fantastic, because they are one of the most talented sides in European football and any coach would love that job.
"If Portugal were to ask? It would be an honour."
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