"I can tell that (FIGC vice chairman Alessandro) Costacurta is a friend and we played together in the national team in 1994," Conte said. "Maybe he forgot that have 18 months with contract at Chelsea and my will and desire is to fulfill this contract."
Previously, it was reported Conte "seems eager" to take back his old position as manager of Italy's national team, according to Italian Football Federation (FIGC) commissioner Roberto Fabbricini.
Conte is one of three major candidates rumoured to be in contention for the role, although Fabbricini told the media there is no favourite to succeed Gian Piero Ventura, per Goal's Sacha Pisani:
"[Roberto] Mancini was in Rome, but we didn't contact him, Conte seems eager to wear Azzurro again, [Carlo] Ancelotti opens and closes the door and [Claudio] Ranieri isn't out either.
"There's no-one in pole position, we have to evaluate the pros and cons.
"We also have to evaluate the availability of the Federation, and explain to those who will come after us that there will be new governance."
The Azzurri are searching for a new boss after Italy failed to qualify for the 2018 FIFA World Cup under Ventura, just the second time in the country's history they've not made it to the showpiece event. The only other World Cup Italy have missed was 60 years ago.
Matt Lewis of Yahoo Sport UK reinforced speculation Conte is unhappy with the transfer business at Chelsea after signing Ross Barkley from Everton, Olivier Giroud from Arsenal and Emerson Palmieri from AS Roma in January:
Fabbricini was speaking to reporters after the FIGC failed to find a replacement for former president Carlo Tavecchio on Thursday.
Conte's place at the Chelsea helm is in doubt as the Premier League champions sit fourth in the table, having slipped 18 points adrift of leaders Manchester City following Wednesday's 3-0 defeat at home to Bournemouth.
Nizaar Kinsella of Goal recently provided quotes from Conte assessing the national team's current position:
Conte managed the Azzurri between 2014 and 2016, at which point he left for Stamford Bridge, having led the national team to a quarter-final finish at that year's European Championship.
For all the recent criticism, however, Chelsea are only three points off second-placed Manchester United and level on points with Liverpool in third, leading BT Sport's Adam Summerton to defend the 48-year-old:
Conte won the Premier League in his debut season in England and previously won three successive Serie A titles with Juventus between 2012 and 2014.
The tactician extended his contract to 2019 last July, but speculation suggests this term could be his last in England's capital.