The Italian has been out of management since leaving Galatasaray in June, and the 49-year-old claims that it would be an "honour" to be offered the Portuguese job.
"Would I go to Portugal? Of course," Mancini told reporters. "If Portugal were to ask? It would be an honour.
"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."
Despite only spending nine months in Istanbul, Mancini did lead Gala to a Turkish Cup success last season.