Zola is firmly in the frame alongside fellow Italian Roberto Donadoni after Slaven Bilic's advisors told West Ham he would not be available until January.
If the current Croatia coach sticks to that timescale then the club will not wait for him, and will look to either Zola or Donadoni, though Michael Laudrup is still in contention too.
Donadoni also made a good impression on Hammers officials when he was interviewed on Friday, while Laudrup will have talks with the club on Monday.
Zola, the former Chelsea midfielder now joint coach of the Italy Under-21 side, does have years of experience in English football under his belt and that stood him in good stead when he met club chiefs in Rome on Saturday morning.
A top-level club source told PA Sport: "Zola not only has impressive credentials but also came across incredibly well in our talks."