Disasi has been frozen out of the Chelsea first team this season, despite training with them at times, and his exit during this winter window was always expected.
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While Chelsea always preferred a permanent sale, they do not hold all the cards and Standard Sport understands West Ham are now hoping to close a deal to sign the Frenchman on a six-month loan.
They are understood to have scheduled a medical for Disasi to take place on the morning of Deadline Day.