Excitation spectra of two-photon excited xenon near the triple point have been obtained in order to study exciton structure near the band edge. While the band gap is suppressed in the low-temperature liquid, absorption due to even-parity exciton states is presented and discussed. The even-parity ${\mathrm{\ensuremath{\Gamma}}}_{3/2}$,n=2 Wannier excitons observed in the liquid are shifted approximately 0.12 eV to higher energies relative to the energy of odd-parity excitons observed in the liquid by Beaglehole. The absorption linewidths (full width at half maximum) are measured to be 0.15 eV. Comparisons are made to one-photon absorption spectra in xenon.