Some architectures of ADC require that the input common-mode voltage of the applied analog signal be within a certain specified range, which is often close to the midpoint of the analog input range.
On the AD7768, AD7768-4, AD7761, and AD7768-1New datasheets the input common-mode voltage range is equal to the supply rails, meaning that there is no specific restriction on the input common-mode voltage. The only restriction is that the absolute input voltages on each of the analog input pins should never exceed the AVDD1 supply voltage or go below the AVSS supply voltage.