  The Upgrade II of the LHCb detector, foreseen for 2031, will operate at an
instantaneous luminosity of 1.5 x 10$^{34}$ cm$^{-2}$s$^{-1}$, accumulating a
sample of more than 300 fb$^{-1}$. To cope with the estimated pile-up of 42 and
200 charged particle tracks per event, precise timing will be added to the
tracking and vertexing sub-systems. A new Vertex Locator (VELO), capable to
manage the expected 7.5-fold increase in data rate, occupancy, and radiation
fluence is needed. Based on a 4D hybrid silicon pixel technology, with enhanced
rate and timing capabilities on the ASIC, the new VELO will allow for precise
beauty & charm hadron identification and real time pattern recognition. Through
detailed simulations, the fluence, inner radius, material budget and pixel size
phase space are explored, while constraining the Impact Parameter (IP)
resolution to the Upgrade I value. Two distinct scenarios emerge as starting
points for further optimizations, with inner radii and end of life fluence of
5.1 mm at 6 x 10$^{16}$ n$_{eq}$/cm$^{2}$ and 12.5 mm at 8 x 10$^{15}$
n$_{eq}$/cm$^{2}$ respectively. Advances and current R&D on sensor
technologies, including LGADs, 3Ds and planar pixels are reviewed, focusing on
radiation hard designs and defect engineering. ASIC related requirements with
respect to sensor capacitance and power budget are taken into consideration for
achieving the 30 ps per hit timing target towards the future 28 nm protype
submission. Improvements in cooling, mechanics and vacuum implementations are
examined with respect to each layout scenario. The use of bi-phasic Krypton
cooling is evaluated as an option for the case of above 1.5 W/cm$^{2}$ power
dissipation. Replaceable sensor modules, coupled with 3D printed titanium
supports are also under consideration. Finally, a comprehensive R&D schedule
towards final design optimization within a six-year period is discussed.
