We prove that the mesoscopic linear statistics $\sum_i f(n^a(\sigma_i-z_0))$
of the eigenvalues $\{\sigma_i\}_i$ of large $n\times n$ non-Hermitian random
matrices with complex centred i.i.d. entries are asymptotically Gaussian for
any $H^{2}_0$-functions $f$ around any point $z_0$ in the bulk of the spectrum
on any mesoscopic scale $0<a<1/2$. This extends our previous result
[arXiv:1912.04100], that was valid on the macroscopic scale, $a=0$, to cover
the entire mesoscopic regime. The main novelty is a local law for the product
of resolvents for the Hermitization of $X$ at spectral parameters $z_1, z_2$
with an improved error term in the entire mesoscopic regime $|z_1-z_2|\gg
n^{-1/2}$. The proof is dynamical; it relies on a recursive tandem of the
characteristic flow method and the Green function comparison idea combined with
a separation of the unstable mode of the underlying stability operator.
