In this paper, I investigate a new non-parametric variable selection framework. To extend the usual non-parametric model, I consider non-linear manifolds which are more flexible. Non-linear manifolds are represented by function compositions, allowing more complex dependences in the data. Based on two manifold approximation techniques , k-nearest neighbours and auto-encoder neural networks, I propose two different procedures to perform non-parametric variable selection. The two methods are complementary , the former being a local estimator, while the latter is a global estimator.