We determined abundances of Na and Zr in the atmospheres of 237 RGB stars in Galactic globular cluster (GGC) 47 Tuc (NGC 104), with a primary goal of searching for possible differences between the abundances of Zr in the first generation (1P) and second generation (2P) stars. For the abundance analysis, we used archival UVES/GIRAFFE spectra obtained during three different observing programmes. Abundances were determined from two NaI and three ZrI lines, using 1D hydrostatic ATLAS9 model atmospheres. The target stars for the abundance analysis were limited to those with 4200<=Teff<=4800K. This is the largest sample of GGC stars in which Na and Zr abundances have been studied so far. While our mean [Na/Fe] and [Zr/Fe] ratios agree well with those determined in the earlier studies, we find a weak but statistically significant correlation in the [Zr/Fe]-[Na/Fe] plane. A comparison of the mean [Zr/Fe] abundance ratios in the 1P and 2P stars suggests a small but statistically significant Zr over-abundance in the 2P stars, {DELTA}[Zr/Fe]_2P-1P_~=+0.06 dex. Also, our analysis shows that stars enriched in both Zr and Na are more centrally concentrated. However, we find no correlation between their distance from the cluster centre and their full spatial velocity, as indicated by the velocity dispersions at different mean values of [Zr/Fe] and [Na/Fe]. While there may be some influence of CN line blends on the determined Zr abundances, it seems very unlikely that the detected Zr-Na correlation, as well as the slightly higher Zr abundances in the 2P stars, would be caused by the CN blending alone. The obtained results indicate that, in 47 Tuc, some amount of Zr should have been synthesised by the same polluters that enriched 2P stars with the light elements. Unfortunately, our data alone do not allow us to distinguish which of the two scenarios, or whether or not a combination of both, could have operated in this GGC.