Mutti, the third coach of the season at the Sicilians, has pick up a single point in his first three games and Zamparini's previous record suggests that, despite his reassuring words earlier this week, the coach may not survive another reverse.
"I have already told Mutti that we still have a lot of work to do," Zamparini said after last week's 1-0 defeat at Chievo.
"Let's say I am worried but am confident, as things can only get better," he said, adding that Mutti's job was safe.
Zamparini took over the club in 2002, when Mutti was in charge, and immediately decided not to renew his contract. Since then, he has presided over more than 20 sackings and resignations of coaches.
Mutti will have seen from the treatment of his predecessor Devis Mangia that Zamparini's declarations of faith can mean exactly the opposite.
Mangia, appointed after Stefano Poli was fired before the season had started, was initially told that Zamparini saw him performing the same type of long-term role that Arsene Wenger has produced at Arsenal.
After some promising results, Mangia's contract was extended for an extra year. One month later, he was sacked and replaced by Mutti.
There have even been rumours that Zamparini could re-appoint Mangia if he tires of the present incumbent, and it would not be unprecedented.
Delio Rossi was sacked last season after a 7-0 home defeat by Udinese but returned one month later after his replacement Serse Cosmi was also dismissed.
Palermo have dropped to 14th with 21 points from 18 games while opponents Genoa are up to eighth.
Unbeaten leaders Juventus, on 38 points, visit Atalanta as the championship reaches the halfway mark.
AC Milan, one point behind in second place, are at relegation-threatened Novara, having needed extra-time to beat the same opponents in the Italian Cup on Wednesday.
Udinese, third with 35 points, host Catania and cannot afford another slip-up after their 3-2 defeat at Genoa.
Fifth-placed Inter Milan, who have won their last six league games including last weekend's derby with Milan, host fourth-placed Lazio.
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