We carried out a multiwavelength cross-correlation analysis of a sample of 16 blazars detected by Fermi/LAT. The purpose is to investigate if there exists correlations between the distinct bands we analyze in this work. We searched for cross-correlated delays between emissions in optical, near-infrared and {\gamma}-ray bands for 16 blazars detected by Fermi-LAT, using three methods previously discussed in the literature: the interpolated cross-correlation function, the discrete cross-correlation function and the Z-transformed discrete cross-correlation function. Our results confirm the expectation that in all our sample the four NIR bands vary simultaneously. For three objects of our sample (3C 273, Mrk 501, and PMN J0808-0751), no correlation is found between any of the bands available for this study. For the remaining thirteen, a correlation was found between the V band and the NIR bands, indicating that in most of them the V band and the NIR bands vary simultaneously. For 4 objects (3C 454.3, PKS 0235+164, PKS 1510-089, and PKS 2155-304) a delayed correlation between the {\gamma}-ray emission and the NIR+V bands was found.