All-optical compact plasma focusing and transportation of electron beams, in the passive mode of a plasma lens, is studied via real geometry particle-in-cell simulations for its suitability for the laser wakefield acceleration technique. The focusing of an electron beam by a passive plasma lens is a non-linear and dynamic process, which strongly depends on the space charge induced evacuation of the plasma electrons in the vicinity of the propagating electron beam. Effects of such focusing on the energy spread, divergence, and emittance of laser-driven electron beams are analyzed numerically for different plasma densities. An initially negative chirp in electron beam energy is shown to be instrumental in suppressing the unwanted growth in the relative energy spread of the electron beam during the passive lensing. Usefulness of such a passive plasma element for a single and multi-stage laser wakefield acceleration configuration is demonstrated.