Italian Domenicali, 55, is set to land the role when chief executive Chase Carey steps down from his position at the end of the year.
The development, which the PA news agency understands has been communicated to the teams but is yet to be confirmed by F1, means the sport will be spearheaded by three former Ferrari chiefs.
Jean Todt is serving his third term as FIA president, while Ross Brawn is the sport’s motorsport boss. The duo oversaw Michael Schumacher’s run of success at Ferrari.
Domenicali was in charge of Ferrari when they won their last constructors’ championship in 2008, but he left the Italian team six years’ later before heading up Lamborghini.
Mercedes boss Toto Wolff, Red Bull team principal Christian Horner and Alejandro Agag, founder of the all-electric championship Formula E, have all been linked with replacing Carey.
Carey, 66, took charge of F1 when Liberty Media completed its takeover in January 2017.
The American, who succeeded Bernie Ecclestone, is expected to remain involved in the sport in some capacity.
