The former Juventus coach replaced Cesare Prandelli at the helm of the national team last summer.
Conte is tied to Italy for another year, and has guided Italy to an unbeaten start to their Euro 2016 qualifying campaign, as they sit two points behind Group H leaders Croatia.
“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 led Juventus to three successive Serie A titles in his three years in charge before stepping down last summer and taking charge of the national side in August.
Italy next face group leaders Croatia in a key encounter in Split on June 12, before they then take on Portugal in an international friendly four days later in Geneva.