Competing endogenous RNAs (ceRNAs) regulate each other by competitively binding microRNAs they share. This is a vital post-transcriptional regulation mechanism and plays critical roles in physiological and pathological processes. Current computational methods for the identification of ceRNA pairs are mainly based on the correlation of the expression of ceRNA candidates and the number of shared microRNAs, without considering the sensitivity of the correlation to the expression levels of the shared microRNAs. To overcome this limitation, we introduced liquid association (LA), a dynamic correlation measure, which can evaluate the sensitivity of the correlation of ceRNAs to microRNAs, as an additional factor for the detection of ceRNAs. To this end, we firstly analyzed the effect of LA on detecting ceRNA pairs. Subsequently, we proposed an LA-based framework, termed LAceModule, to identify ceRNA modules by integrating the conventional Pearson correlation coefficient and dynamic correlation LA with multi-view non-negative matrix factorization. Using breast and liver cancer datasets, the experimental results demonstrated that LA is a useful measure in the detection of ceRNA pairs and modules. We found that the identified ceRNA modules play roles in cell adhesion, cell migration, and cell-cell communication. Furthermore, our results show that ceRNAs may represent potential drug targets and markers for the treatment and prognosis of cancer.