The Colombian is a transfer target for Los Blancos, per the Daily Mail's Simon Jones.
There's no doubting his ability. Falcao is a fantastic finisher, and we've seen from his time at Atletico Madrid that he can cut it in Spain.
He notched 28 goals in 35 games in La Liga before moving to France. That included three goals in four games against Real Madrid and Barcelona, Atletico's two main La Liga rivals.
He would also be able to settle in the Spanish capital, having lived there before while playing for Real's rivals.
However, there are two obvious negative possibilities with Falcao.
A year in the French league, still a rung below La Liga and the Premier League, may have dulled his predatory instincts.
Falcao scored nine for Monaco last season in 17 Ligue 1 games, which is decent going but nothing special. In his last 10 games for the French outfit, he had only notched twice.
Also, the knee injury he sustained against Toulouse on January 19 may have a long-lasting impact.
If he was close to being fully fit then he would have made Colombia's World Cup squad, so Madrid may not have him for the start of the season.
And what if his knee injury has detracted from him physically or psychologically?
We've seen plenty of players come back from injury and fail to regain their previous form.
It would be a gamble for Real Madrid to splash the cash on Falcao when they don't know how he will recover from the damage done.
Karim Benzema played well last season and arguably had his finest campaign in a Madrid shirt.
While he wasn't always as clinical as he should have been, his all-round game came on leaps and bounds.
A player like Benzema can bring out the best in Cristiano Ronaldo and Gareth Bale, whereas Falcao will be the centrepiece of the attack.
While he is supremely talented, it might not necessarily be the best thing for the club.
All this said, adding Falcao to the squad would hardly harm Madrid's chances of lifting the trophy, provided they kept Benzema.
"I can't wait to get to Turin. Everyone has told me it's a great city and I am looking forward to getting to know it."
The young Spaniard's departure means that Madrid could do with another forward.
Falcao offers something different to Benzema, something more physical and a more ruthless edge.
If Falcao is the Falcao we know and love, he may be able to help fire Madrid to La Liga glory.
But to bank on it could prove to be an expensive gamble.
Of course, Real Madrid won the Champions League last season and have never been ones to let money prove an obstacle between them and their targets.
It would not be a surprise if they splashed out on Falcao and he helped them regain the title from their city rivals, Atletico.
But equally, it's not something they should necessarily expect to happen if they do purchase the Colombian.