It is well known that some orthogonal polynomials can be expressed in terms of Hermite polynomials taking limits in some of the parameters. Two of the most remarkable examples are the limit relations between the Jacobi and Laguerre polynomials and the Hermite polynomials. In this paper, we advance in this sense and establish a more general method which allows us to obtain asymptotic expansions of classical orthogonal polynomials in terms of the Hermite ones. By means of these asymptotic expansions, we can easily obtain well known limits between the polynomials of the Askey table and to obtain some near ones. In this paper we express the asymptotic representation of the Charlier polynomials in terms of Hermite polynomials and show some numerical experiments about the approximation convergence.