A supervised machine learning (ML) based computational methodology for the design of particulate multifunctional composite materials with desired thermal conductivity (TC) is presented. The design variables are physical descriptors of the material microstructure that directly link microstructure to the material's properties. A sufficiently large and uniformly sampled database was generated based on the Sobol sequence. Microstructures were realized using an efficient dense packing algorithm, and the TCs were obtained using our previously developed Fast Fourier Transform (FFT) homogenization method. Our optimized ML method is trained over the generated database and establishes the complex relationship between the structure and properties. Finally, the application of the trained ML model in the inverse design of a new class of composite materials, liquid metal (LM) elastomer, with desired TC is discussed. The results show that the surrogate model is accurate in predicting the microstructure behavior with respect to high-fidelity FFT simulations, and inverse design is robust in finding microstructure parameters according to case studies.