Hammers director Mike Lee confirmed Zola and Donadoni were leading candidates.
Lee told BBC Radio Five Live: "We have a very strong shortlist and it's going to be a tough decision with some exciting candidates.
"From the meetings that have taken place so far the two that have really shone have been Donadoni and Zola.
"We have been surprised and pleased by the number of applications we have had and we are moving towards a short shortlist and ideally have a manager in place in time for the West Brom match next week.
"Slaven Bilic could potentially be on that shortlist but it depends very much upon his availability. If for whatever reason he was not available until January in terms of working with us I'm afraid that will rule him out."