The COVID-19 pandemic has clearly brought the healthcare systems worldwide to a breaking point, along with devastating socioeconomic consequences. The SARS-CoV-2 virus, which causes the disease, uses RNA capping to evade the human immune system. Nonstructural protein (nsp) 14 is one of the 16 nsps in SARS-CoV-2 and catalyzes the methylation of the viral RNA at N7-guanosine in the cap formation process. To discover small-molecule inhibitors of nsp14 methyltransferase (MTase) activity, we developed and employed a radiometric MTase assay to screen a library of 161 in-house synthesized S-adenosylmethionine (SAM) competitive MTase inhibitors and SAM analogs. Among six identified screening hits, SS148 inhibited nsp14 MTase activity with an IC50 value of 70 ± 6 nM and was selective against 20 human protein lysine MTases, indicating significant differences in SAM binding sites. Interestingly, DS0464 with an IC50 value of 1.1 ± 0.2 µM showed a bisubstrate competitive inhibitor mechanism of action. DS0464 was also selective against 28 out of 33 RNA, DNA, and protein MTases. The structure–activity relationship provided by these compounds should guide the optimization of selective bisubstrate nsp14 inhibitors and may provide a path toward a novel class of antivirals against COVID-19, and possibly other coronaviruses.