The hyperfine structure (hfs) of electron levels of 23892U ions with the nucleus excited in the low-lying rotational 2(+) state with an energy E(2(+)) = 44.91 keV is investigated. In hydrogenlike uranium, the hfs splitting for the 1s(1/2) ground state of the electron constitutes 1.8 eV. The hyperfine-quenched (hfq) lifetime of the 1s2p 3P0 state has been calculated for heliumlike 23892U and was found to be 2 orders of magnitude smaller than for the ion with the nucleus in the ground state. The possibility of a precise determination of the nuclear g(r) factor for the rotational 2(+) state by measurements of the hfq lifetime is discussed.