The Colombia international has been linked with a big-money move away from the Ligue 1 side, despite signing a five-year deal upon completing a €60 million switch from Porto last summer.
Monaco recently insisted their prized asset - who has just returned from a cruciate knee ligament injury - would not be leaving the club, but Falcao's father left the door open to a transfer.
“I’m not saying he [Falcao] will leave. I’m only saying that he has a contract with Monaco,” Radamel Garcia told Cadena Cope.
“My son has never told me that he wants to go from Monaco, but, with him I don’t talk about football.
“My son has a contract for four years [at Monaco] and he is serving it.
When asked about Falcao potentially playing under Carlo Ancelotti at the Santiago Bernabeu next year, Garcia added: “If my child ought to play or not [at Real], depends on Ancelotti.”
Falcao, 28, made his long-awaited return from injury when Monaco played out a 2-2 draw with Valencia in the Emirates Cup in London last week.
The Colombia international missed his nation’s World Cup campaign in Brazil this summer after suffering an anterior cruciate ligament injury in his left knee in January.