The recent discovery of high-${T}_{c}$ superconductivity near 80 K in the bilayer nickelate ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ has attracted widespread attention. The prerequisite to understanding the unconventional superconductivity in ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ is the determination of the electronic properties, such as the band structure and possible correlation effect. Here, we report a set of data on single-particle tunneling measurements on ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ single crystals at ambient pressure. A gaplike feature was observed in the tunneling spectra at low energies around the Fermi energy. The spectrum looks roughly symmetric with gap edges at about $+98$ and $\ensuremath{-}92$ meV. We attribute this gaplike feature to two alternative origins: either reflecting the bonding and antibonding bands derived from the Ni-$3{d}_{{z}^{2}}$ orbital, or a mixed contribution from a density wave gap and these two bands. Meanwhile, a finite density of states remains even in the gapped region, which is thought to be the vestige contribution of the $\mathrm{Ni}\text{\ensuremath{-}}3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbital. Furthermore, it is found that the density of states is suppressed in a wide energy range with a sharp rise at about $\ifmmode\pm\else\textpm\fi{}1.4$ eV, indicating a general correlation effect. Theoretical calculations give partial consistency with the experimental observations. Our results provide important information to understand the electronic states of ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ at ambient pressure.