Italy's Football Federation (FIGC) approached Carlo Ancelotti before contacting Pep Guardiola about the vacant national team coaching position.
Ancelotti signed a contract extension with the Brazil Football Confederation (CBF) in May through to the 2030 World Cup with the Italian having taken charge of the national team shortly after leaving Real Madrid a year earlier.
Italy's new technical director Paolo Maldini, who played with Ancelotti and was later coached by him from 2001 until 2009 at AC Milan, told reporters on Thursday: "Before speaking to Pep, I also spoke to Carlo Ancelotti.
"It seemed right to us to start with those we consider to be the best in the world. We need to check their general availability first, and then the rest."
Under Ancelotti, Brazil crashed out of the World Cup after a 2-1 round-of-16 defeat to Norway.
Both the CBF and Ancelotti confirmed that despite the World Cup disappointment, they would continue working together.
Italy have been without a coach since Gennaro Gattuso resigned after April's World Cup playoff loss to Bosnia and Herzegovina that saw the Azzurri miss out on a third consecutive men's World Cup.
Guardiola, who left Manchester City after 10 successful years in England, is among the candidates that the FIGC are considering for the role.
Maldini denied reports that the Spaniard is requesting a €20m annual salary to guide Italy, which is reportedly double what the FIGC are willing to offer.
"For Pep, the financial aspect is not a factor at all," he said.
Former Italy coach Roberto Mancini, who guided the Azzurri to Euro 2020 glory, and 2006 World Cup winner Andrea Pirlo are also contenders.
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The FIGC are hoping to announce the new coach by the end of this week.
"Ideally, we'd like to wrap things up by the end of this week, but perhaps it would be even better to wait for the person we want," Maldini said. "The timing depends on whether we can secure the person we want. There's a sense of urgency, but deep down we're not in such a rush."
Italy are in need of a major shake-up and Giovanni Malagò, who was elected FIGC president on June 22, on Thursday spoke about the project to rebuild the national team.
"The target we have set ourselves is six years, leading up to the 2032 European Championship, by which time we must close this glaring gap that is plain for all to see," he said. "We need to rebuild the path from the ground up."
