The involvement of genes and miRNAs in the development of atherosclerosis is a challenging problem discussed in recent publications. It is necessary to establish which miRNAs affect the expression of candidate genes. We used known candidate atherosclerosis genes to predict associations. The quantitative characteristics of interactions of miRNAs with mRNA candidate genes were determined using the program, which identifies the localization of miRNA binding sites in mRNA, the free energy interaction of miRNA with mRNA. In mRNAs of
GAS6
and
NFE2L2
candidate genes, binding sites of 21 miRNAs and of 15 miRNAs, respectively, were identified. In
IRS2
mRNA binding sites of 25 miRNAs were located in a cluster of 41 nt. In
ADRB3, CD36, FASLG, FLT1, PLA2G7
, and
PPARGC1A
mRNAs, clusters of miR-466, ID00436.3p-miR, and ID01030.3p-miR BS were identified. The organization of overlapping miRNA binding sites in clusters led to their compaction and caused competition among the miRNAs. The binding of 53 miRNAs to the mRNAs of 14 candidate genes with free energy interactions greater than −130 kJ/mole was determined. The miR-619-5p was fully complementary to
ADAM17
and
CD36
mRNAs, ID01593.5p-miR to
ANGPTL4
mRNA, ID01935.5p-miR to
NFE2L2
, and miR-5096 to
IL18
mRNA. Associations of miRNAs and candidate atherosclerosis genes are proposed for the early diagnosis of this disease.