Classical nanopore sensing relies on the measurement of the ion current passing through a nanopore. Whenever a molecule electrophoretically translocates through the narrow constriction, it modulates the ion current. Although this approach allows one to measure single molecules, the access resistance limits the spatial resolution. This physical limitation could potentially be overcome by an alternative sensing scheme taking advantage of the current across the membrane material itself. Such an electronic readout would also allow better temporal resolution than the ionic current. In this work, we present the fabrication of an electrically contacted molybdenum disulfide (MoS2) nanoribbon integrated with a nanopore. DNA molecules are sensed by correlated signals from the ionic current through the nanopore and the transverse current through the nanoribbon. The resulting signal suggests a field-effect sensing scheme where the charge of the molecule is directly sensed by the nanoribbon. We discuss different sensing schemes such as local potential sensing and direct charge sensing. Furthermore, we show that the fabrication of freestanding MoS2 ribbons with metal contacts is reliable and discuss the challenges that arise in the fabrication and usage of these devices.