A new instrument is under development for the high luminosity upgrade of the Large Hadron Collider at CERN (HL-LHC) to provide non-invasive beam size measurements throughout the acceleration cycle. The Beam Gas Vertex (BGV) detector consists of a very low pressure gas target inside the beam pipe with a series of particle tracking stations located downstream. Inelastic collisions between the beam and the gas target produce secondary particles which are detected by the tracking stations. The beam size is measured from the spatial distribution of several thousand beam-gas interaction vertices, which are identified by means of the reconstructed tracks. A demonstrator device, operated over the past 3 years, has proven the feasibility of the BGV concept and has motivated development of a fully operational device for the HL-LHC. The status of current design studies for the future instrument will be presented, with particular emphasis on potential tracking detector technologies, readout schemes, and expected performance.