To every complex manifold $X$, we may assign its tangent bundle $TX$ (which is also in correspondence with its tangent sheaf $\mathcal{T}_X$). The idea here is that we can parametrize the tangent spaces of $X$ in a smooth fashion using the smooth structure of $X$ itself (via the Jacobian of the transition maps).
I am interested in knowing if there is an analog of this for arbitrary complex analytic spaces, the barrier here being that the dimension of the tangent space can vary from point-to-point. I am familiar with the concept of 'linear spaces' (in the sense of Grauert), and I am wondering if to every complex analytic space we may assign some 'linear space' that works similarly to the tangent bundle. That is, I would like to associate to a complex analytic space $X$ some linear space $TX$ over $X$ that parametrizes the tangent spaces of $X$ using the analytic structure of $X$, in particular, if $X$ is smooth then $TX$ should be the usual tangent bundle.
Any knowledge of whether or not this is possible would be greatly appreciated! References are also appreciated.
I am relatively new to the theory of complex analytic spaces, so forgive me if my language was a bit imprecise.