The Italy international was flagged as a primary target for new Blues boss Antonio Conte, who had relied on Candreva during his time in charge at italy.
However the west London club appear to have missed out on the 29-year-old, who is on the verge of joining Inter.
The San Siro side have agreed a deal worth around £17.75m up front with a further £2.5m to follow in bonuses.
And, according to the Gazzetta dello Sport, Candreva has agreed personal terms in Milan and will undergo a medical this week before the deal can be rubber-stamped.
It has even been suggested that Candreva has requested the No.87 shirt number for his new side.