The Spanish giants are believed to be close to securing a deal to bring the Colombian to the Bernabeu, despite Monaco insisting that their highly-rated striker is not for sale
The Colombia international has expressed his desire to return to Spain following an injury-interrupted season at AS Monaco.
Goal can confirm an outline agreement has been reached, with further discussions over the transfer fee planned.
Though his current contract does not specify a release fee, it was signed last May on the understanding that Falcao would be permitted to leave the club should an attractive offer emerge at the end of his first season there.
Monaco will expect Madrid to match the €60million transfer fee they paid to sign the former Porto striker from Atletico, although, publicly at least, the Ligue 1 club remain adamant they will not be selling their star striker this summer.
“There are no negotiations with any club for Falcao," said Monaco’s vice president Vadim Vasilyev on Thursday.
Asked if Falcao had asked to leave, he replied: "We have not talked about that. We count on him and believe he will have a great season in 2014-2015.
"Nobody is not transferable, I don't know of any examples in football - yet there is no discussion, we rely on him."
The 28-year-old missed his nation's impressive run to the World Cup quarter-finals after damaging his left anterior cruciate ligament during a French Cup tie in January, and the transfer to Madrid is being delayed by his rehabilitation from that setback.
Madrid's medical department have taken a cautious approach to assessing the player's recovery, requesting that they be granted the opportunity to see Falcao on the pitch before green lighting the move.
Madrid president Florentino Perez is a long standing admirer of Falcao, having attempted to prise the forward from Atletico Madrid during a two-season spell in which he scored 70 goals in 91 appearances for their cross-city rivals.
Atletico, however, refused to allow their leading scorer to join Madrid, paving the way for a move to newly enriched Monaco instead.
Falcao has scored 153 times in 197 club matches in the five seasons since he left South America for Porto, winning back-to-back Europa Leagues and four national trophies.