Italy are still reeling from their historic failure to qualify for the 2018 World Cup finals after Sweden beat them in the play-offs on Monday.
Heartbroken Italians are looking for some immediate positive response, and Allegri, who won the Italian title in 2011 at AC Milan and the last three at Juventus, would fit the bill.
“Coaching the national team is one of my ambitions, but not right now,” the 50-year-old told a press conference ahead of Juventus's game at Sampdoria on Sunday.
“In a few years,” said the man who made his name as coach at Cagliari and who is known as tactically astute.
“I still have major objectives to attain with Juventus, building a team for the future.”
“As for the national team we can talk about that in a few years time, if indeed I ever get offered the job,” said Allegri, who took over Juventus in 2014.
Italy is still floundering in disbelief after 75,000 stunned fans in Milan's San Siro Stadium and 14.8 million horrified Italians watched their national fall from grace at the hands of Sweden on Monday.
Italy had only failed once before to make the cut, at the Sweden finals of 1958.
The Italian football federation called crisis talks on Wednesday and sacked the 69-year-old Gian Piero Ventura.
With his avuncular touch the former Bayern Munich, Real Madrid, AC Milan, Chelsea, PSG and Juventus coach Carlo Ancelotti is the favourite to take over and rebuild the Azzurri.