Let Vp(λ) be the class of all functions f defined on the open unit disc D of the complex plane having simple pole at z= p, p∈ (0 , 1) and analytic in D { p} satisfying the normalizations f(0) = 0 = f′(0) – 1 such that | (z/ f(z)) 2f′(z) – 1 | < λ for z∈ D, λ∈ (0 , 1]. In this article, we obtain sharp bounds of the Zalcman and the generalized Zalcman functionals for functions in Vp(λ) for some indices of these functionals. As consequences of the obtained results, we pose the Zalcman-like coefficient conjectures for this class of functions. In addition, we estimate bound for the generalised Fekete–Szegö functional along with bounds of the second- and the third-order Hankel determinants for this class of functions.