The London outfit have faltered this campaign as they lie fifth in the standings, 19 points behind leaders Manchester City, leading to uncertainty over Conte's future.
"I haven't chosen yet but I think Conte is the one who could do the best," Former AC Milan defender Costacurta told Italian newspaper Gazzetta dello Sport on Tuesday.
"(Conte) has already shown he knows how to be national team coach while the others haven't yet."
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Costacurta added that ex-Manchester City boss Roberto Mancini and former AC Milan manager Carlo Ancelotti are also being considered for the national team role.
Italy sacked Gian Piero Ventura in November after the team failed to qualify for the 2018 World Cup in Russia with under-21 coach Luigi Di Biagio currently in charge as interim manager.
Italy, who will miss the global tournament for the first time since 1958, face Argentina and England in international friendlies next month.
(Reporting by Aditi Prakash in Bengaluru)
