Differential beamforming combined with microphone arrays can be used in a wide range of applications related to acoustic and speech signal acquisition and recovery. A practical and useful method for designing differential beamformers is the so-called null-constrained method, which was developed based on linear arrays and requires only the nulls' information from the target directivity pattern. While it is effective and easy to use, this method is found not suitable for designing steerable differential beamformers with circular arrays. This paper reexamines this technique in the context of circular differential microphone arrays. By analyzing the properties of the circular array topology, the null-constrained method is extended to include symmetric constraints, which is inherent in the design of circular arrays. This extension yields a design method for fully steerable differential beamformers that require only minimum information from the target beampattern. Simulations justify the theoretical analysis and demonstrate the good properties of the developed method.