We systematically search for magnetic flux rope structures in the solar wind to within the closest distance to the Sun of 0.13 AU, using data from the third and fourth orbits of the Parker Solar Probe. We extend our previous magnetic helicity based technique of identifying magnetic flux rope structures. The method is improved upon to incorporate the azimuthal flow, which becomes larger as the spacecraft approaches the Sun. A total of 21 and 34 magnetic flux ropes are identified during the third (21 days period) and fourth (17 days period) orbits of the Parker Solar Probe, respectively. We provide a statistical analysis of the identified structures, including their relation to the streamer belt and heliospheric current sheet crossing.