The Lincoln Institute of Land Policy has a data set and a paper detailing land cover for a range of cities. They did good work on estimating the amount of land taken by those cities.
We created a new data set comprising the universe of all 3,649 named metropolitan agglomerations and cities that had populations in excess of 100,000 in the year 2000, their populations in that year, and their built-up area identified in the MOD500 map, currently the best satellite-based global map of urban land cover.
They find increasing rates of urban sprawl:
we found that average density in the built-up areas of a global sample of 120 cities declined at a mean annual rate of 2.0 percent between 1990 and 2000.
Land is more and more inefficiently used. In particular, “urban land cover in Sub Saharan African will increase more than 12-fold between 2000 and 2050.” So in fact as population grows the amount of land per capita increases over time.
The whole paper here.