In this work, we present a modification to the digital Wallace-based Gaussian Random Number Generator (GRNG) by implementing an in-memory memristive dot-product engine in place of the vector-matrix multiplication (VMM) stage. The dot-product engine provides an analog interface to the GRNG with statistical robustness and better resource efficiency. One modification with three different structures is proposed and evaluated by the statistical test pass rates and benchmarked against the digital implementations. The best-proposed modification achieved a 95.8% test pass rate for 100 iterative small pool generation while requiring 23.6% and 44.4% less power and area consumption.