The appointment will be announced in the near future, the report said.
According to several Italian journalists, the parties are considering signing a three-year contract or a two-year contract with a one-year extension clause.
Genoa is currently managed by Davide Ballardini. Genoa now holds 15th position in Serie A.
The Italian club is owned by U.S. private investment firm 777 Partners, which acquired a controlling stake from the former owner, Enrico Preziosi.