The Italian coach was heavily backed in the summer transfer window, with over £200M spent on new players, but the start to the campaign has been poor.
Spurs are yet to score a league goal and they have already been knocked out the Carabao Cup by Liverpool.
Ahead of a crunch clash with fellow winless wonder Aston Villa, former Spurs keeper Kasey Keller claimed the run of games in October after the incoming international break will decide if De Zerbi stays in post.
"The start of November is probably where I'm looking at. Watching the match the other day vs. Everton, they should've been up 3-0 at half-time," Keller told Express Sport on behalf of Casinostugan.
"When you now go four games at the start of the season without scoring in the first time in Spurs' history, there's not going to be a lot of patience.
"Spurs fans would be more patient if you lost 4-3 rather than drawing 0-0, so that's the tricky part. You've spent a lot of money, and many of us are still questioning where is that marquee striker?
"From what they created at the weekend, they should've won the match comfortably, and they didn't, so something has to click quickly."
On their return to action, Spurs have four matches in October, away at Manchester United and Chelsea plus home ties with Coventry City and Crystal Palace.