The Gunners will have money to spend, having just signed a British record £150million sponsorship deal with Puma.
They will replace Nike next season, and the cash injection will reportedly give Arsene Wenger £100million to spend on new players.
Falcao has been heavily linked with Chelsea in the past, but completed a £51million move to Monaco in the summer.
However, the former Atletico Madrid forward has already been linked with a move away after failing to settle in France.
He is also likely to miss the remainder of this season, after coming off worse in a heavy challenge during Monaco’s French Cup clash with Chasselay.
The Colombian’s World Cup dreams are thought to be hanging by a thread, having recently undergone successful knee surgery.
The Gunners may attempt to lure him to London at the end of the season, with a big money offer.
Falcao is also sponsored by Puma, so the sponsorship deal may aid a possible bid.