While many large earthquakes are preceded by observable foreshocks, the mechanism responsible for the occurrence of these smaller‐scale seismic events remains uncertain. One physical explanation of foreshocks with growing support is that they are produced by the interaction of slow slip with fault heterogeneity. Inspired by the suggestion from laboratory experiments that foreshocks occur on fault asperities (bumps), we explore rate‐and‐state fault models with patches of higher normal stress embedded in a larger seismogenic region by conducting 3‐D numerical simulations of their behavior over long‐term sequences of aseismic and seismic slips. The models do produce smaller‐scale seismicity during the aseismic nucleation of larger‐scale seismic events. These smaller‐scale events have reasonable stress drops, despite the highly elevated compression assigned to the source patches. We find that the two main factors contributing to the reasonable stress drops are the significant extent of the rupture into the region surrounding the patches and the aseismic stress release just prior to the seismic events. The smaller‐scale seismicity can only occur if a sufficient separation in nucleation scales between the foreshock‐like events and mainshocks is achieved. Our modeling provides insight into the conditions conducive for generating foreshocks on both natural and laboratory faults.