The paper focuses on the problem of time consistency of an interval Shapley-like value in cooperative interval dynamic games. This problem has not been investigated in the game theory literature for the considered class of dynamic games. It is proved that the interval Shapley-like value is time inconsistent, and to satisfy the time consistency condition for the interval value, it is necessary to introduce a new control variable, so-called imputation distribution procedure. The imputation distribution procedure is proposed in an explicit form.
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