The process $e^+e^-rightarrow poverline{p}pi^0$ has been studied by analyzing data collected at $sqrt{s}=3.773$ GeV, at $sqrt{s}=3.650$ GeV, and during a $psi(3770)$ line shape scan with the BESIII detector at the BEPCII collider. The Born cross section of $p overline{p} pi^0$ in the vicinity of the $psi(3770)$ is measured and the Born cross section of $psi(3770)rightarrow p overline{p} pi^0$ is extracted considering interference between resonant and continuum production amplitudes. Two solutions with the same probability and a significance of 1.5$sigma$ are found, and the Born cross section of $psi(3770)rightarrow p overline{p} pi^0$ is determined to be less than 0.22 pb at 90% confidence level and $33.8pm1.8pm2.1$ pb, respectively. Using the estimated cross section and a constant decay amplitude approximation, the cross section $sigma(poverline{p} rightarrow psi(3770) pi^0)$ is calculated for the kinematic situation of the planned $overline{text{P}}text{ANDA}$ experiment. The maximum cross section corresponding to the two solutions is expected to be less than $0.79$ nb at 90% confidence level and $122pm10$ nb at a center of mass energy of 5.26 GeV.
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