"I would like to see a female European Commission president.
"The issue is not an old versus a new name, but about personalities, strategic vision and ability," he said on the sidelines of the European Council meeting in Brussels.
Conte said he "respects" German Chancellor Angela Merkel but understood she was "not available" for the role of European Commission chief.
A marathon 18-hour summit session broke up in acrimony on Monday, with no agreement over a reported French-German compromise deal on the new head of the European Commission, the bloc's executive arm.
Under the reported deal, Dutch Labour leader Frans Timmermans would head the Commission with centre-right Bulgarian Kristalina Georgieva taking the other key job of European Council President.
That deal fell apart when the four Visegrad states of Poland, Hungary, Czech Republic and Slovakia blocked the plan, with the backing of Italy.
Timmermans has riled the Visegrad countries with his softer approach to migration as commission Vice President over the last five years. The Italian government, which includes the anti-migrant League party, shares some of this anger.
Female contenders for European Commission presidency include outgoing EU Competition Commissioner Margrethe Vestager, Green Party MEP Ska Keller and Lithuanian President Dalia Grybauskaite.
( With inputs from IANS )