With the rapid growth of audio and video applications on the internet, caching media objects in transcoding proxies has become an important research topic in recent years. In this paper, we address the problem of finding the optimal locations for placing fixed number of transcoding proxies among the nodes in a network such that the specified objective is achieved. We present an original model for this problem, which makes transcoding proxy placement decisions on all the en-route nodes along the routing path in a coordinated way. In our model, proxy status information along the routing path of requests is used for optimally determining the locations for placing fixed number of transcoding proxies. We formulate this problem as an optimization problem and the optimal locations are obtained using a low-cost dynamic programming-based algorithm. We implement our algorithm and evaluate our model on different performance metrics through extensive simulation experiments. The implementation results show that our model significantly outperforms the random algorithm which places transcoding proxies among the nodes in a network randomly.