The 25-year-old is keen to leave the Turin giants and the west Londoners have offered him a possible escape route as they search for a midfielder in the final hours of transfer deadline day.
A medical in Turin has been completed by Zakaria with a £26million purchase option included in the deal.
It comes amid Chelsea’s struggles to sign a new midfielder late in the summer window after Thomas Tuchel expressed his concerns over mounting injuries.
Ajax have rejected a £40million bid from Chelsea for Mexico international midfielder Edson Alvarez, while an approach for Ibrahim Sangare has also been snubbed by PSV Eindhoven.
With Mateo Kovacic not fully fit plus N'Golo Kante and Ruben Loftus-Cheek injured, the Blues are concerned about their options despite still having Conor Gallagher and Jorginho available, plus £35m of youth midfielders beneath them in Carney Chukwuemeka and Cesare Casadei.
The Blues have also agreed a fee with Brighton for Billy Gilmour who is set to complete a medical and move to the south coast.