  Using $N_f=2+1$ QCD calculations at physical quark mass and purely imaginary
baryon chemical potential, we locate Lee-Yang edge singularities in the complex
chemical potential plane. These singularities have been obtained by the
multi-point Pad\'e approach applied to the net baryon number density. We
recently showed that singularities extracted with this approach are consistent
with universal scaling near the Roberge-Weiss transition. Here we study the
universal scaling of these singularities in the vicinity of the QCD critical
endpoint. Making use of an appropriate scaling ansatz, we extrapolate these
singularities on $N_\tau=6$ and $N_\tau=8$ lattices towards the real axis to
estimate the position of a possible QCD critical point. We find an approach
toward the real axis with decreasing temperature. We compare this estimate with
a HotQCD estimate obtained from poles of a [4,4]-Pad\'e resummation of the
eighth-order Taylor expansion of the QCD pressure.
