  We develop a QCD sum rule analysis of the form factor
$F_{\gamma^*\gamma^*\pi^0}(q^2,Q^2)$ in the region where virtuality of one of
the spacelike photons is small $q^2 \ll 1 GeV^2$ while another is large: $Q^2
\gapprox 1 GeV^2$. We construct the operator product expansion suitable for
this kinematic situation and obtain a QCD sum rule for
$F_{\gamma^*\gamma^*\pi^0}(0,Q^2)$. Our results confirm expectation that the
momentum transfer dependence of $F_{\gamma^*\gamma^*\pi^0}(0,Q^2)$ is close to
interpolation between its $Q^2=0$ value fixed by the axial anomaly and $Q^{-2}$
pQCD behaviour for large $Q^2$. Our approach, in contrast to pQCD, does not
require additional assumptions about the shape of the pion distribution
amplitude $\varphi_{\pi}(x)$. The absolute value of the $1/Q^2$ term obtained
in this paper favours $\varphi_{\pi}(x)$ close to the asymptotic form
$\varphi_{\pi}^{as} (x)=6 f_{\pi} x (1-x)$.
