The Spanish giants are keen to add reinforcements to their attack and have highlighted both players as potential targets.
And current first-choice striker Karim Benzema’s form has been inconsistent so far this campaign, leading club chiefs to look at options to bolster their squad.
Spanish outlet Sport report that Los Blancos are looking to bring in a striker without spending huge sums.
Club President Florentino Perez has identified Ibrahimovic and Falcao as two figures who could be acquired for relatively little outlay, rather than fork out on a future forward.
Ibrahimovic is currently plying his trade in the MLS for L.A Galaxy, whilst Falcao is at French Ligue 1 side Monaco.
It is thought Ibrahimovic, 37, could be attained on a free transfer, which appeals to Madrid.
Despite being in his twilight years, the Swedish hitman is in good form, having scored 22 goals for Galaxy since his move to the United States.
Falcao is not quite as simple, given he is under contract till 2020, and Monaco would command a substantial fee for his services.
It is thought Madrid would be against paying a significant sum for a 33-year-old.
The Colombian has netted four times in 11 appearances for the French club so far this season.