Massimiliano Allegri wants to stay at AC Milan for a long time amid reports linking him with the Italy job, though he would not totally rule out leading the national team.

Italy are searching for a new head coach following the departure of Gennaro Gattuso on Friday, after they failed to qualify for a third straight edition of the World Cup.

The Azzurri were beaten on penalties by Bosnia-Herzegovina following a 1-1 draw in their play-off final in Zenica on Tuesday, with Francesco Pio Esposito and Bryan Cristante missing from the spot.

They are the first former world champions to miss three consecutive World Cups, having only failed to appear at two of the first 20 editions of the competition.

And Allegri – who has Milan in contention for the Scudetto in his first season back in charge of the Rossoneri – believes root and branch reform is required to make them competitive again.

However, at least for the time being, he does not intend to be part of their rebuild.

"I haven't thought about it yet," Allegri said when asked about the Italy job on Saturday, ahead of Monday's meeting with Napoli in Serie A.

"I am at Milan, I am happy here, and I hope to be here for a long time. We started with the objective of qualifying for the Champions League, which is a fascinating tournament that I have not participated in for a while. I'd like to participate in it with Milan.

"The national team's problem is not just about the coach; the entire system needs to find solutions. 

"It is not all to be thrown away, because even when things are going badly, there is always something you can build on."

But when asked again if he could manage the national team in the future, Allegri said: "Life is unpredictable, you never know what could happen."

Gattuso was one of several key figures to leave the Italy setup this week, with Italian Football Federation (FIGC) president Gabriele Gravina and head of delegation Gianluigi Buffon also resigning.

"I am sad about the World Cup, but I think everyone should take this as an opportunity to grow," Allegri added.

"There are those whose jobs it is to get together, examine the rules, see what can be done, from the very foundations of academies to the first team.

"I don't think it can all be sorted out in 10 minutes. We need time to create a united front of ideas so we can be in the best condition to reach the World Cup in 2030.

"We do have good players in Italy, and I think the future is in good hands. I repeat, it is not about the coach, there are many things to be examined before 2030."