According to The Sun, The Blues believe they can get Robinson for the fee Leeds had agreed with Aston Villa last summer after Rennes yesterday turned down a £6.5m bid for Czech keeper Petr Cech.
The report suggests Ranieri wants 24-year-old Robinson to compete with current No 1 Carlo Cudicini and will offer reserve Neil Sullivan as part-exchange.
Villa chairman Doug Ellis stopped Robinson's move to Villa, when he refused to match his alledged £22k-a-week Elland Road contract.