The Azzurri have yet to find a replacement for Gian Piero Ventura, who was relieved of his duties after failing to secure qualification for the 2018 World Cup.
Various names have been offered as contenders to fill the void, with Conte one of those to have been heavily linked with a second spell at the helm.
He continues to see questions asked of his future in England, and has admitted that he intends to head home at some stage, and Costacurta has talked up his claims to a return to international coaching.
The former Italy defender, who is now vice-commissioner to the Italian Football Federation (FIGC), told Gazzetta dello Sport: “Of all the potential candidates, for me, Antonio Conte would be the best.
“I’m sure we will find a new man within a couple of months.”
He added: “I have not made my final decision yet.
“Conte has already been in charge of the national team but that does not mean that I will ignore people like Roberto Mancini, Carlo Ancelotti or even the likes of Claudio Ranieri, Gian Piero Gasperini or Marco Giampaolo. They would all do well.”
While there are several options under consideration, one man who is not in the running is AC Milan boss Gennaro Gattuso.
The former midfielder, who represented his country on 73 occasions in his playing days, has made a positive start to a spell in charge at the San Siro.
He has rejuvenated Milan, but Costacurta says a former team-mate is not yet ready to take the biggest job in Italian football.
He added: “I have said already and I’ll say it again, no. It’s too early for him and we have not had any contact.”