  We extend our analysis of quasi-distributions onto the pion distribution
amplitude. Using the formalism of parton virtuality distribution amplitudes
(VDAs), we establish a connection between the pion transverse momentum
dependent distribution amplitude (TMDA) $\Psi (x, k_\perp^2)$ and the pion
quasi-distribution amplitude (QDA) $Q_\pi (y,p_3)$. We build models for the
QDAs from the VDA-based models for soft TMDAs, and analyze the $p_3$ dependence
of the resulting QDAs. As there are many models claimed to describe the
primordial shape of the pion DA, we present the $p_3$-evolution patterns for
models producing some popular proposals: Chernyak-Zhitnitsky, flat and
asymptotic DAs. Our results may be used as a guide for future studies of the
pion distribution amplitude on the lattice using the quasi-distribution
approach.
