According to the reports, Giuliani has shown interest in leading Team Melli.
The 59-year-old has recently coached Turkey national volleyball team.
Iran parted company with Behrouz Ataei in October following poor results in the 2023 Volleyball Nations League.
Italian coach Angelo Lorenzetti, Roberto Piazza, Russian Vladimir Alekno, Belgian Vital Heynen and Saeid Marouf are the other candidates for the job.
Iran's chances of reaching the 2024 Paris Olympics are slim due to poor results in the 2023 FIVB Volleyball Nations League and the Olympic qualifiers.