The report claims the Colombian will not play for Real Madrid as the Bernabeu club feel he's too expensive, but he still wants to leave Monaco after less than 12 months at the French club.
Chelsea and Manchester City were linked with Falcao before he joined Monaco, and Mendes wants to see if they're still keen.
His €14m-a-year salary plus €50m transfer fee are potential stumbling blocks, although Chelsea and Manchester City are two of only a handful of clubs in the world that could afford such an outlay.
His Atletico connections hinder Real Madrid's chances of signing him, and the report claims only a limited pool of clubs are interested - with Real Madrid priced out of a move.
Those are PSG, City and Chelsea - the Blues are managed by Jose Mourinho, who is also represented by Mendes.
Falcao reportedly wants out of Monaco, but only Cristiano Ronaldo earns more per season than the Colombian at €14m-a-year.
He wants to play for one of the biggest clubs in Europe, and with the French state poised to alter their tax structure to take up to 75 per cent of earnings over a million euros, the Colombia international has instructed Mendes to explore alternatives.
Manchester City were linked with Falcao before they moved for Alvaro Negredo and Steven Jovetic, and with Edin Dzeko and Sergio Aguero on the books as well, it's unlikely they would be interested in another forward.
Chelsea, in contrast, are lacking a world-class forward. Although Fernando Torres is showing signs of getting back to his best, Demba Ba and Samuel Eto'o have so far failed to effectively spearhead the Blues attack.