The computational cost in analyzing a dynamical system increases with the dimension of the model. This cost further increases where repeated solutions for different parameter values of the system are required, such as uncertainty quantification and optimization. In recent years, a proper orthogonal decomposition (POD)-based reduced order model (ROM) has been developed that reduces the cost significantly. This ROM is intrusive in nature, that is, it requires access to the computer codes used for solving the high-dimensional model. However, for many complex problems such as soil-structure interaction (SSI), such access is not available, which poses a limitation to the ROM. To address this issue, a non-intrusive ROM is developed in this work that does not require access to the source codes. The objective of this paper is to develop a non-intrusive ROM for SSI problems considering uncertainty in the excitations that can be further used for the uncertainty quantification of SSI under earthquake load or random excitations. This ROM is developed using deep neural networks. The application of neural networks makes the model learn features of an earthquake excitation efficiently. Finally, the accuracy of the proposed ROM is tested numerically on a beam on Winkler foundation.