Gian Piero Ventura was sacked in November after the 1-0 play-off loss to Sweden meant the four-time World Cup winners failed to qualify for the finals for the first time since 1958.
Luigi Di Biagio, the Under-21 boss, has been handed the reins on an interim basis while the Italian Football Federation seeks a permanent successor, with the likes of Carlo Ancelotti, Antonio Conte and Roberto Mancini reportedly in the frame.
Ranieri, who joined Nantes ahead of this season, said he will leave if offered the Italy job, and the Canaries' president Waldemar Kita says the club will not stand in his way.
"If the situation presented itself, which is not the case, I would discuss it with him of course because he is a gentleman who has a huge experience in international football," Kita said, in quotes reported by L'Equipe.
"And I would understand in some way that a high-level career ends on an opportunity that will not be presented twice.
"So we would have to analyse it and see how we can organise it to not leave the club in a difficult situation on the day that it would be decided, but for now, that is not the case, there are several candidates.
— FC Nantes (@FCNantes) February 19, 2018
Claudio Ranieri pic.twitter.com/iKlWzbV0OU
"Taking a team from his country is a dream for any coach and I don't like to curb someone's career. We would have to adapt, and do what we can do."