Zola has led West Ham to the verge of European qualification
West Ham will face a hearing at the end of the season to decide if they will be granted a Uefa licence for next season.
The licence, which permits clubs to play in European competition, can only be given when specific financial documents are submitted by the club.
West Ham's financial problems and the potential for a change of ownership means these have not been submitted.
The Hammers remain confident that they will be in a position to do so on 26 May, the day of the hearing.
A statement from the Football Association read: "The FA can confirm that, following initial consideration of West Ham United's application, the club has not to date been granted a Uefa licence to compete in European competition next season should they qualify.
"In accordance with set procedures, a final hearing will take place on May 26 before a panel appointed by Sport Resolutions - an independent specialist alternative dispute resolution body."
West Ham are currently seventh in the Premier League and challenging for a place in next season's Europa League.
However, it was revealed on Wednesday that the personal debt of chairman Bjorgolfur Gudmundsson stands at £300m and that a consortium of creditors led by Icelandic bank Straumur - which is itself in financial difficulties - is in talks about taking over the club.
"Due to a number of factors, principally relating to a possible change of ownership of West Ham United, the club has not been able to submit certain financial information, but expects to be in a position to do so by May 26," read a statement from the club.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.