Say $V$ is a topological vector space. What conditions do you need to add on $V$ to make it a (topological, maybe infinite-dimensional) manifold?
For instance, can we view the Schwartz class functions, test function spaces, or distributions as being locally homeomorphic to a Banach space?
In the finite-dimensional case, there's only one topological vector space in each dimension (up to continuous isomorphism), so there's no ambiguity about what's meant by an "$n$-dimensional manifold," at least in the topological sense. But in the infinite-dimensional case, things are very different. There isn't one definition of "infinite-dimensional manifold" -- instead, one chooses a particular topological vector space $V$ as a model, and then defines a class of infinite-dimensional manifolds as spaces that are locally homeomorphic to $V$. In particular, people commonly study Banach manifolds, Hilbert manifolds, and Fréchet manifolds, modeled after topological vector spaces of the indicated types.
So the answer to your question is, in a certain tautological sense, yes: if $V$ is a topological vector space, then there is a class of manifolds modeled on $V$, and $V$ itself is certainly one of them.