We investigate in detail "instantaneous interquark potentials," interesting gauge-dependent quantities defined from the spatial correlators of the temporal link-variable U(4), in generalized Landau gauge using SU(3) quenched lattice QCD. The instantaneous Q (Q) over bar potential has no linear part in the Landau gauge, and it is expressed by the Coulomb plus linear potential in the Coulomb gauge, where the slope is 2-3 times larger than the physical string tension. Using the generalized Landau gauge, we find that the instantaneous potential can be continuously described between the Landau and the Coulomb gauges, and its linear part rapidly grows in the neighborhood of the Coulomb gauge. We also investigate the instantaneous 3Q potential in the generalized Landau gauge, and obtain similar results to the Q (Q) over bar case. T-length terminated Polyakov-line correlators and their corresponding "finite-time potentials" are also investigated in generalized Landau gauge.