Recent work on non-autoregressive neural machine translation (NAT) that leverages alignment information to explicitly reduce the modality of target distribution has reported comparable performance with counterparts that tackle multi-modality problem by implicitly modeling dependencies. Effectiveness in handling alignment is vital for models that follow this approach, where a token reordering mechanism is typically involved and plays a vital role. We review the reordering capability of the respective mechanisms in recent NAT models, and our experimental results show that their performance is sub-optimal. We propose to learn a non-autoregressive language model (NALM) based on transformer which can be combined with Viterbi decoding to achieve better reordering performance. We evaluate the proposed NALM using the PTB dataset where sentences with words permuted in different ways are expected to have their ordering recovered. Our empirical results show that the proposed method can outperform the state-of-the-art reordering mechanisms under different word permutation settings, with a 2-27 BLEU improvement, suggesting high potential for word alignment in NAT.