We propose a new DNA sequencing concept based on nonradiative Förster resonant energy transfer (FRET) from a donor quantum dot (QD) to an acceptor molecule. The FRET mechanism combined with the nanopore-based DNA translocation is suggested as a novel concept for sequencing DNA molecules. A recently-developed hybrid quantum/classical method is employed, which uses time-dependent density functional theory and quasistatic finite difference time domain calculations. Due to the significant absorbance of DNA bases for photon energies higher than 4 eV, biocompatibility, and stability, we use Zinc-Oxide (ZnO) QD as a donor in the FRET mechanism. The most sensitivity for the proposed method to DNA is achieved for the Hoechst fluorescent-dye acceptor and 1 nm ZnO-QD. Results show that the insertion of each type of DNA nucleobases between the donor and acceptor changes the frequency of the emitted light from the acceptor molecule between 0.25 to 1.6 eV. The noise analysis shows that the method can determine any unknown DNA nucleobases if the signal-to-noise ratio is larger than 5 dB. The proposed concept and excellent results shed light on a new promising class of DNA sequencers.