Solution processed graphene variants including graphene oxide (GO) and reduced graphene oxide (RGO) are promising materials for potential optoelectronic applications. To date, efficiency of the excitation energy transfer into GO and RGO thin layers has not been investigated in terms of donor-acceptor separation distance. In the present work, we study nonradiative energy transfer (NRET) from CdSe/CdS quantum dots into single and/or double layer GO or RGO using time-resolved fluorescence spectroscopy. We observe shorter lifetimes as the separation distance between the QDs and GO or RGO decreases. In accordance with these lifetimes, the rates reveal the presence of two different mechanisms dominating the NRET. Here we show that excitonic NRET is predominant at longer intervals while both excitonic and nonexcitonic NRET exist at shorter distances. In addition, we find the NRET rate behavior to be strongly dependent on the reduction degree of the GO-based layers. We obtain high NRET efficiency levels of similar to 97 and similar to 89% for the closest separation of the QD-RGO pair and the QD-GO pair, respectively. These results indicate that strong NRET from QDs into thin layer GO and RGO makes these solution-processable thin films promising candidates for light harvesting and detection systems.