This paper aims to design an optimal interval observer for discrete linear time-invariant (LTI) systems. Particularly, the proposed design method first transforms the interval observer into a zonotopic set-valued observer by establishing an explicit mathematical relationship between the interval observer and the zonoptopic set-valued observer. Then, based on the established mathematical relationship, a local optimal observer gain is designed for the interval observer via the equivalent zonotopic set-valued observer structure and the Frobenious norm (F-norm) based size of zonotopes. Third, considering that the dynamics of the optimal interval observer becomes a discrete linear time varying (LTV) system owing to the designed timevarying optimal gain, an optimization problem to obtain a coordinate transformation matrix and the local optimal observer gain for the interval observer is formulated and handled. Finally, a theoretic comparison on the conservatism of the interval observer and the zonotopic set-valued observer is made. At the end of this paper, a microbial growth bioprocess is used to illustrate the effectiveness of the proposed method.