The former Newcastle and Tottenham manager had 12 months in charge of Ghana before being axed in January 2024.
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Hughton now is the leading candidate to take the Zimbabwe job.
The FA want their new coach installed in time to prepare for December's Africa Cup of Nations in Morocco.
ZIFA president Nqobile Magwizi said: “The process of appointing the Warriors coach is at an advanced stage.
“We will announce the appointment by next Monday, or Tuesday at the latest.”