Recent theoretical findings suggest that the local flexibility of a polymer, linked to the chemical details of the molecule, can affect both the position and the size of knots along the polymer itself. Being of relevance in biology and material science, we further investigate this issue by performing molecular dynamics simulations on a model of diblock flexible stiff polymer ring hosting a trefoil knot. We show that when both blocks are sufficiently long to accommodate the knot, by raising the temperature T, one may shift the knot position from the flexible part to the stiffer one. Even a very short flexible region has a high probability of lying within the knotted portion at lower temperatures. In addition, we observe that there is a tendency for either extremities of the knot to pin at the interface of the two blocks. This correlation between knot position and bending inhomogeneity supports the view that enzymes, binding the DNA in proximity of single-stranded gaps and nicks, have a better chance to alter the global topology of the chain. Finally, we observe that knots, initially squeezed within flexible portions shorter than the typical knot size, may give rise to long-lived metastable states.