The magnetic-loop Wichmann-Kroll (WK) corrections to the hyperfine splitting of the 1s and 2s states and the corresponding corrections to the nuclear magnetic moments were calculated. These corrections were included in the calculation of the hyperfine splitting values of heavy Li-like ions based on the experimental values of the hyperfine splitting in the corresponding H-like ions. It was found that the magnetic-loop WK correction affects the 1s and 2s hyperfine splitting in a similar manner and, thus, hardly improves the total theoretical predictions for the hyperfine splitting in lithiumlike ions.