"(I) say to all those jealous people wanting this job: they have to fight for it!" Domenicali told F1's official website last week.
According to Gazzetta, however, 48-year-old Domenicali might finally be losing the support of Ferrari president Luca di Montezemolo.
Montezemolo left the Bahrain circuit last Sunday part-way through the grand prix, declaring that watching "slow" Ferraris gave him "great pain".
Now, at an event at the Ferrari museum in Maranello on Friday, Montezemolo reportedly said: "I already know what you want to ask.
"My reply is that we will leave no stone unturned to be where we need to be. We will work day and night to improve and make the decisions that we need to take."
Wondered Gazzetta correspondent Andrea Tosi: "(Will there be) changes at the top of the Gestione Sportiva?"