Very large reflector antennas are often analyzed as quasi-optical systems in two main steps. In the first stage, the field is propagated from the feed to the equivalent aperture, while in the second, the radiation pattern is computed by aperture integration, which for planar apertures can be accelerated using the Fast Fourier Transform (FFT) (R. E. Collin, Antennas and Radio Wave Propagation. New York: McGraw-Hill, 1985). The recently developed far-field Multi-Level Physical Optics (MLPO) algorithm (A. Boag and C. Letrou, IEEE Trans. Antennas Propagat., vol. 53, pp. 2064-2072, 2005) facilitates the fast computation of the radiation patterns from given field distributions on non-planar surfaces, thus obviating the need to use planar equivalent apertures that introduce additional phase errors (R. E. Collin, Antennas and Radio Wave Propagation. New York: McGraw-Hill, 1985). In order to improve the far sidelobe accuracy, the Physical Theory of Diffraction (PTD) line integral can be included in these computations (C. Letrou and A. Boag, IEEE Trans. Antennas and Propagation, vol. 60, pp. 1182-1186, 2012). In this paper we focus on the first step of the analysis involving the field propagation to the main reflector, which subsequently serves as a non-planar radiating aperture for the far-field MLPO computation. Conventionally, the field originating from the feed is propagated through successive reflections within a multi-reflector antenna using Geometrical Optics (GO)-based ray tracing. Such GO modeling completely neglects the effects of finite wavelength on the field distributions, thus resulting in significant errors. As an alternative, we propose a numerically efficient near-field MLPO algorithm for accurate field propagation in multi-reflector systems. To that end, a near-field version of the MLPO algorithm for field propagation between reflectors is developed and combined with the earlier developed generalized far-field MLPO. The computational complexity of the near-field MLPO is comparable to that of its far-field counterpart. The performance of the proposed method is studied on the example of RATAN-600 radio telescope antenna.