The shortlist was put together from a list of 37 prospective candidates, unusually all named on the Ivorian Football Federation's website (www.fif-ci.com).
A decision on the new coach must now be taken by the federation's executive committee, who have previously promised to announce their final choice by the end of the month.
Fernandez, who won 60 caps and a European Championship title with France, last worked as national team coach of Israel but has been a radio pundit for the last three years.
Renard won the African Nations Cup with Zambia two years ago but last season, failed to save Sochaux from relegation from Ligue 1 after being brought in for the second half of the campaign.
Gillot was coach of Girondins Bordeaux last season while Antonetti has had a long career as a coach in Ligue 1, most recently with Stade Rennes.
The new Ivory Coast coach will take over from Sabri Lamouchi, whose two-year contract was not renewed after the country failed to reach the second round at the World Cup in Brazil.
In September, the Ivorians begin the qualifiers for next year's Nations Cup in Morocco.
(Reporting by Mark Gleeson in Cape Town; Editing by John O'Brien)
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