The winger is in the final stages of officially becoming a Blues player, with Mohamed Salah set to join the Italian outfit on an 18-month loan deal.
Cuadrado, who had been attracting interest from Manchester United, will become Jose Mourinho's first signing of the winter transfer window, although the Portuguese tactician is not planning on bringing any more players to Stamford Bridge this month.
Andre Schurrle is also on the brink of leaving west London, with a £22m move to Wolfsburg set to be completed by tomorrow.