The sensitive information present in the training data, poses a privacy concern for applications as their unintended memorization during training can make models susceptible to membership inference and attribute inference attacks. In this paper, we investigate this problem in various pre-trained word embeddings (GloVe, ELMo and BERT) with the help of language models built on top of it. In particular, firstly sequences containing sensitive information like a single-word disease and 4-digit PIN are randomly inserted into the training data, then a language model is trained using word vectors as input features, and memorization is measured with a metric termed as exposure. The embedding dimension , the number of training epochs, and the length of the secret information were observed to affect memorization in pre-trained embeddings. Finally, to address the problem, differentially private language models were trained to reduce the exposure of sensitive information.