The problem of interval state observer design is addressed for time-invariant discrete-time systems. Two solutions are proposed: the first one is based on a similarity transformation synthesis, which connects a constant matrix with its nonnegative representation ensuring the observation error positivity. The second contribution shows that in discrete-time case the estima-tion error dynamics always can be epresented in a cooperative form without a transformation of coordinates. The corresponding observer gain can be found as a solution of the formulated LMIs. The performances of the proposed observers are demonstrated through computer simulations.