This paper deals with the relationship between the intrinsic randomness (IR) problem and the fixed-length source coding problem. The IR problem is one of random number generation problems and optimum achievable rates (optimum IR rate) with respect to several approximation measures such as the variational distance, the Kullback-Leibler (KL) divergence and f-divergences, have been investigated. In particular, it has been shown that the optimum IR rate with respect to the variational distance has a close relationship with the supremum of the unachievable rate in the source coding problem. Inspired by this result, in this paper, we consider the optimum IR rate with respect to a subclass of f-divergences and try to show a relationship with the unachievable rate in the source coding problem. The subclass of f-divergences considered in this paper includes several well-known measures, such as the variational distance, the KL divergence, the Hellinger distance. We also consider a class of normalized f-divergences, which includes the normalized KL divergence.