The Colombia international has emerged as the Londoners’ major January target over the course of the past week, with negotiations with La Viola rumbling away.
A fee is yet to be agreed with the Serie A side, however reports claim that personal terms have been settled on with the wide-man.
Fiorentina are adamant they want his full £26.8m release clause paid, but Chelsea are eager to drive the price down.
Mohamed Salah may even be used as a makeweight in a deal, with the Egyptian having struggled to make an impact at Stamford Bridge since his move 12 months ago.
Andre Schurrle may also be sold, with Wolfsburg thought to be closing in on his signature.