You can do the next best think. To a Forman-Morse function $f$ one can associate a flow on the manifold whose stationary points are precisely the barycenters of the faces of your simplicial decomposition. The Conley index of the barycenter of a critical face has the homotopy type of a sphere of the dimension of that face. The Conley index of the barycenter of a non-critical face is homotopically trivial.
Additionally, one can construct a continuous function $\tilde{f}$ on the manifold that decreases along the trajectories of this flow and hose values at a barycenter is equal to the value of $f$ on the corresponding face.
For details see Chapter 11 of this paper. The faces of the barycentric subdivision of your simplicial complex are invariant sets of this flow, and on such a face the flow is depicted in Figure 2, p.16 of the above paper.
It took me a while to realize that in Morse theory the gradient flow associated to a Morse function is more important than the function itself. The function plays a sort of accounting role and the Morse condition restricts the nature of the stationary points of the gradient flows.
Remark A while ago I asked this question on MathOverflow that is related to the abundance of discrete Morse functions. They are extremely rare as opposed to the usual smooth Morse functions that are generic.