Both Sky Sport Italia and Mediaset have reported that a meeting was held not far from the Italian FA’s headquarters in the capital to discuss terms with Ancelotti, who was sacked by Bayern Munich in September but is still under contract.
The meeting, which lasted just over an hour and a half, is expected to help Costacurta complete his search for a new coach by his May 20 deadline.
Costacurta set that deadline to prepare for Italy’s friendlies with Saudi Arabia, France and Netherlands at the end of May and start of June, and then this autumn’s Nations League and qualifiers for Euro 2020.
Ventura was sacked in November following Italy’s failure to qualify for the World Cup and former under-21s coach Luigi Di Biagio led the team in friendlies against Argentina and England in March.
Former Manchester City manager Roberto Mancini had been regarded as the leading candidate in recent months, with Ancelotti stating his preference to return to club management and being linked with the Arsenal job.