Antonio Conte wants to remain in charge of Italy beyond Euro 2016 and has asked for a two-year contract extension, according to Italian Football Federation president Carlo Tavecchio.
The former Juventus coach replaced Cesare Prandelli at the helm of the national team last summer.
Italy are unbeaten under Conte, who is tied to the Azzurri for another year.
"Conte has asked me to extend his contract for a further two years," Tavecchio told the Italian press. "I'm delighted with his request because as everyone knows, I worked hard to get Conte.
"But I can only make commitments during my term as president, not after.
"It's something that we will consider further on."
Conte, 45, led Juve to three straight Scudetti in his three years in charge before stepping down last summer.
Italy are second in Euro 2016 qualifying group H, two points adrift of leaders Croatia, who they face in Split on June 12.
The Azzurri will then take on Portugal in an international friendly four days later in Geneva.