The AS Monaco forward is seemingly available for transfer, either on loan for a fee of anywhere between £12 million and £20 million, or can be purchased on a permanent basis for a significantly larger sum.
Reports in France imply that it is Juventus, rather than the cash-rich City or resurgent force Arsenal, who have the upper hand in negotiations as they are the only interested club to make an official offer.
The Old Lady of Serie A are rumoured to have made a bid for a one-year loan deal, with a clause embedded into the deal that could allow them to buy Falcao at the end of the season.
Both Manchester City and Arsenal have been blighted by an injury to a key player - Alvaro Negredo and Olivier Giroud, respectively - and the addition of Falcao would no doubt remedy their woes.
The Premier League pair have until the evening of September 1 to complete business, however, they may now need to press forth and make an improved offer to ensure that the penalty-box poacher does not return to the Italian division.
Do you think Manchester City or Arsenal have a chance to sign Radamel Falcao or is he destined for a Serie A return, albeit with Juventus?