The Goodison Park outfit were looking to bring the Belgian international to England on a season-long deal, with an option to make the transfer permanent.
Everton have claimed that the necessary forms were submitted before last Friday's 11pm deadline, but FIFA have refused to clear the move.
A statement on the Toffees official website read: "FIFA have today refused to ratify the loan transfer of Vadis Odjidja-Ofoe to Everton from Club Brugge.
"The decision comes despite both the Football Association and Premier League giving their full support to the loan agreement and Everton lodging the relevant signed paperwork in advance of the international transfer deadline on August 31.
"An Everton spokesman confirmed the club will consider all available options before making any further comment."
Vadis Odjidja-Ofoe has been capped three times at international level.