Benzema’s form has dipped this season, with the Frenchman scoring only two La Liga goals so far.
Marca reports that Madrid has now finalised four key targets to upgrade the position.
Inter Milan hit man Mauro Icardi, Arsenal star Alexis Sanchez and RB Leipzig forward Timo Werner are the alternatives.
It is understand that the club could go for a player, that will be able to rotate in and out with Lucas Vazquez and Marco Asensio in the wide areas, but also provide a penalty area presence.
Sanchez will be available for free next summer, while the Nerazzurri has put a €100m price tag on Icardi. Werner could, however, arrive this month.