The La Liga champions are locked in a battle with Manchester City, Chelsea and Paris St Germain for Falcao, but if they are successful, Benzema could prove surplus to requirements at the Bernabeu.
Gunners boss Arsene Wenger is believed to be a keen admirer of the France international, and the report suggests the Arsenal manager has been linked with bids for the Real Madrid striker in the past.
The 24-year-old would be the odd one out if Madrid signed Falcao, as Jose Mourinho's side already have Gonzalo Higuain and Cristiano Ronaldo.
Higuain and Benzema have battled for much of the past year for the sole starting spot up front, and the Argentinian looks to have come out of top, starting and scoring most recently at the weekend as Madrid beat Celta Vigo 2-0.
And Spanish newspaper El Mundo Deportivo reports Mourinho would be willing to offload the former-Lyon striker, which could alert long-term admirers Arsenal.
The Gunners sold captain Robin Van Persie in August to Manchester United, and Wenger reportedly has a significant transfer budget for the coming January transfer window.
But talkSPORT reports Arsenal would have to compete with PSG for the signature of Benzema. The big-spending French club are thought to have approached Real Madrid over the France international during the summer, but were rebuffed.
The capture of Falcao from Atletico Madrid could change their stance.