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In this work, we study a new text mining problem of discovering named entities with temporally correlated bursts of mention counts in multiple multilingual Web news streams. Mining named entities with temporally correlated bursts of mention counts in multilingual text streams has many interesting and important applications, such as identification of the latent events, attracting the attention of on-line media in different countries, and valuable linguistic knowledge in the form of transliterations. While mining "bursty" terms in a single text stream has been studied before, the problem of detecting terms with temporally correlated bursts in multilingual Web streams raises two new challenges: (i) correlated terms in multiple streams may have bursts that are of different orders of magnitude in their intensity and (ii) bursts of correlated terms may be separated by time gaps. We propose a two-stage method for mining items with temporally correlated bursts from multiple data streams, which addresses both challenges. In the first stage of the method, the temporal behavior of different entities is normalized by modeling them with the Markov-Modulated Poisson Process. In the second stage, a dynamic programming algorithm is used to discover correlated bursts of different items, that can be potentially separated by time gaps. We evaluated our method with the task of discovering transliterations of named entities from multilingual Web news streams. Experimental results indicate that our method can not only effectively discover named entities with correlated bursts in multilingual Web news streams, but also outperforms two state-of-the-art baseline methods for unsupervised discovery of transliterations in static text collections.