Variants that alter the DNA-binding specificity of transcription factors could affect the specificity for and expression of potentially many target genes, as has been observed in several tumor-derived mutations. Here we examined if such trans expression quantitative trait loci (trans-eQTLs) could similarly result from common genetic variants. We chose to focus on the Cys2-His2 class of zinc finger transcription factors because they are the most abundant superfamily of transcription factors in human and have well-characterized DNA binding interactions. We identified 430 SNPs that cause missense substitutions in the DNA-contacting residues. Fewer common missense SNPs were found at DNA-contacting residues compared to non-DNA-contacting residues (P = 0.00006), consistent with possible functional selection against SNPs at DNA-contacting positions. Functional predictions based on ZNF DNA binding preferences also suggested that many common substitutions could potentially alter binding specificity. However, Hardy-Weinberg Equilibrium analysis and examination of seven orthologs within the primate lineage failed to find evidence of trans-eQTLs associated with the DNA-contacting positions, nor evidence of a difference selection pressure on a contemporary and evolutionary timescales. The overall conclusion was that common SNPs that alter the DNA-contacting residues of these factors are unlikely to produce strong trans-eQTLs, consistent with the observations by others that trans-eQTLs in humans tend to be few and weak. Some rare SNPs might alter specificity, and remained rare due to purifying selection. The study also underscores the need for large-scale eQTLs mapping efforts that might provide experimental evidence for SNPs that alter the choice of transcription factors binding sites.