It had been expected that the Algerian forward would complete a transfer to Merseyside for a reported fee of £10.4m, but it appears that the deal may now be scrapped.
According to BBC Sport, negotiations have come to a halt and it is now considered doubtful that the move will be finalised.
Everton boss Ronald Koeman allegedly has a war chest of £50m for the January transfer window, and he has already spent over half of that to complete the signings of Morgan Schneiderlin and Ademola Lookman.
Belfodil - who can count Inter Milan and Parma among his previous clubs - had expected to be the next man through the door at Goodison Park until this latest development.
He has scored nine goals in 19 appearances this season, including three in the Europa League.