  The quantum time of arrival (TOA) problem requires statistics of the measured
arrival times given only the initial state of a particle. Following the
standard framework of quantum theory, the problem translates into finding an
appropriate quantum image of the classical arrival time $\mathcal{T}_C(q,p)$,
usually in operator form $\hat{\mathrm{T}}$. In this paper, we consider the
problem anew within the phase space formulation of quantum mechanics. The
resulting quantum image is a real-valued and time-reversal symmetric function
$\mathcal{T}_M(q,p)$ in formal series of $\hbar^2$ with the classical arrival
time as the leading term. It is obtained directly from the Moyal bracket
relation with the system Hamiltonian and is hence interpreted as a Moyal
deformation of the classical TOA. We investigate its properties and discuss how
it bypasses the known obstructions to quantization by showing the isomorphism
between $\mathcal{T}_M(q,p)$ and the rigged Hilbert space TOA operator
constructed in [Eur. Phys. J. Plus \textbf{138}, 153 (2023)] which always
satisfy the time-energy canonical commutation relation (TECCR) for arbitrary
analytic potentials.
