Napoli coach Antonio Conte would be willing to take the vacant Italy job with his club president Aurelio De Laurentiis supporting the move on Tuesday.
Gennaro Gattuso resigned as Azzurri boss on Friday after Italy failed to reach this summer's World Cup for a third straight time.
Conte's deal at Napoli runs until 2027 with the Italian champions seven points off Serie A leaders Inter Milan with seven matches of the season remaining.
"It's expected that my name appears on the list of candidates for the national team," Conte told reporters after Monday's 1-0 league win over AC Milan.
"If I was the federation's president, I would consider my name.
"But, you know my contractual situation, I'll meet with my president at the end of the season and we will see," the 56-year-old added.
Conte was in charge of the four-time World Cup winners between 2014 and 2016 when he led the team to Euro 2016 where they were eliminated on penalties by Germany in the quarterfinals.
He led Napoli to last season's Scudetto but was close to leaving the Stadio Diego Armando Maradona in the summer after a fall-out with De Laurentiis.
Gattuso left the job 24 hours after Gabriele Gravina resigned as the head of the Italian football federation (FIGC).
"If Conte asked me to allow him to become the national team coach again, I would say yes," De Laurentiis told website Calcionapoli24.
"But as he's very intelligent, as long as there's no (FIGC) president, and up to now there hasn't been, I don't think he sees himself in charge of something so disorganised," Laurentiis added.
AC Milan boss Massimiliano Allegri has also been linked with the Azzurri position but Gattuso's replacement will not be named until after June 22's FIGC extraordinary meeting, to elect a new president for the body.