Former Italian goalkeeper Zenga took over the reins at the start of the season looking to carry on the work of Sinisa Mihajlovic, who led Sampdoria to a seventh place finish and a potential Europa League place before moving to AC Milan.
Sampdoria's hopes of qualifying for Europe's second tier competition were ended by a 4-0 defeat at home to Vojvodina in preliminary round.
And after a promising start to life in Serie A, the Genoa-based club have dropped steadily down the table.
On Sunday, Fiorentina handed Sampdoria their fourth defeat of the season, and their first at home, to regain top spot in Italy with Zenga's men dropping to 10th place, 11 points adrift.
Some hardline supporters called on club president Massimo Ferrero to sack Zenga, claiming the former Inter Milan great – who made 58 appearances for Italy and came to be known as 'L'Uomo Ragno' (Spider Man) – isn't up to the job.
Some reports claim Ferrero will give Zenga until the away trip to Udinese in a fortnight, following the international break, before making any decision on the 55-year-old's future.
However, Sky Sport Italia claims Ferrero could act in a matter of hours, with former club coach Gigi Delneri reportedly in the frame.
According to the website of Gazzetta dello Sport, Ferrero attempted to call Zenga to his office on Monday to sack him only to discover the coach had decided to benefit from the break for international football to fly to Dubai for a short holiday.
The report said Zenga “could now be fired by email”.