The Colombian is one of the most sought after forwards in Europe, following successful spells with Porto and current club Atletico Madrid.
His most recent ground-breaking performance came last the weekend, as he hit five goals as in a 6-0 victory over Deportivo.
Chelsea have been chasing Falcao for some time now and see him as the ideal replacement for Fernando Torres, who has failed to impress since his £50m arrival in 2011.
However, Real Madrid boss Jose Mourinho believes that he can persuade the South American to move across the Spanish capital in January and is willing to part with the £45m fee demanded by his employers.
The 26-year-old’s ownership status may leave Atletico powerless to resist a big money bid, despite claims that he is not for sale.
It is believed that an investment fund own 50% of Falcao’s rights and would have a major say in whether he is allowed to move on. The companies involved stand to make a significant profit should a near £50m move materialise.
Losing him will be a big blow to Atletico’s hopes of gaining Champions League qualification, with the striker having hit 19 goals in 15 appearances this term.