Let S(p) represent the collection of meromorphic univalent functions f in the unit disc D which possess a simple pole at z=p(0<p<1) and meet the normalization f(0)=f′(0)-1=0. In this article, we determine bounds for Hermitian Toeplitz determinants whose entries are the Taylor coefficients of functions in S(p). Furthermore, we derive bounds for Hermitian Toeplitz determinants for two specific subclasses of S(p).