The Moon generated a long-lived core dynamo magnetic field, with intensities at least episodically reaching ~10­­–100 µT during the period prior to ~3.56 Ga.  While magnetic anomalies observed within impact basins are likely attributable to the presence of impactor-added metal, other anomalies such as those associated with lunar swirls are not as conclusively linked to exogenic materials. This has led to the hypothesis that some anomalies may be related to magmatic features such as dikes, sills, and laccoliths. However, basalts returned from the Apollo missions are magnetized too weakly to produce the required magnetization intensities (>0.5 A/m).  Here we test the hypothesis that subsolidus reduction of ilmenite within or adjacent to slowly cooled mafic intrusive bodies could locally enhance metallic FeNi contents within the lunar crust.  We find that reduction within hypabyssal dikes with high-Ti or low-Ti mare basalt compositions can produce sufficient FeNi grains to carry the minimum >0.5 A/m magnetization intensity inferred for swirls, especially if ambient fields are >10 μT or if fine-grained Fe-Ni metals in the pseudo-single domain grain size range are formed.  Therefore, it is plausible that the magnetic sources responsible for long sublinear swirls like Reiner Gamma and Airy may be magmatic in origin.  The results of this study will help guide interpretations of lunar crustal field data acquired by future rovers that will traverse lunar magnetic anomalies.