The mechanical properties of composite materials strongly depend on their microstructure, and their spatial variability is often modeled as random property fields. Conventional approaches for constructing such fields from microstructure images rely on extracting numerous stochastic volume elements (SVEs) and performing repeated finite element–based numerical homogenization, which leads to significant computational cost. Recent studies have introduced convolutional neural networks (CNNs) as surrogate models for SVE-level homogenization[1]; however, these approaches typically focus on local predictions and do not explicitly learn mappings at the field level. This study explores the potential of Neural Operators for directly learning mappings from microstructure images to spatially varying elastic property fields. Neural Operators are designed to learn operators between function spaces and are therefore a promising candidate for modeling spatially correlated material properties. In this work, we formulate an operator-learning framework in which the input is a microstructure data of a two-phase composite and the output is a corresponding elastic property field obtained via numerical homogenization. The framework does not necessarily rely on moving-window procedures or explicit SVE partitioning. The objective of this study is to investigate the potential of applying operator learning to microstructure-informed random field modeling. Specifically, we explore the applicability of operator-learning approaches to stochastic homogenization problems and discuss their validity and potential effectiveness.