The Neapolitans have struggled to obtain results consistently and they squandered the lead late on Wednesday evening when they drew 3-3 away to Sassuolo.
According to Corriere della Sera, the relationship between Napoli president Aurelio De Laurentiis and the technical staff further deteriorated after the draw with Neroverdi.
The Ciucciarelli patron will consider sacking both his coach and sporting director if the squad suffers a defeat against Bologna on the weekend.
Gattuso is contracted until the end of June but the Partenopei might end the working relationship before then. Although Giuntoli’s contract does not expire until June 2024, this might not save him from suffering the same fate as Gattuso.
Napoli are sixth in Serie A with 44 points from 24 matches and they also have a game in hand.