No. And, in particular, not soon. Given the currently available and foreseeable technologies, the energy requirement for the sustained flight of whole cities would be much too high. The mass of an entire infrastructure of buildings, streets, etc. is, after all, gigantic. Hence, the amount of energy needed to lift such structures into the air, and keep them there, would also be gigantic. There is also the question of why we would want to do this. What advantages would flying cities offer?
We are also still far from having the whole human race, or even a significant proportion of the world’s population, living in space. But the question remains: Apart from individual astronauts conducting research, why would this be needed? Even if there were a good reason, we don’t have the technology to send more than just a few representatives of humankind into orbit each year. This is mainly because the energy expended to send people into space is still much greater than that used to get an aeroplane off the ground. What is indeed interesting, although not yet a tangible possibility, is the concept of space elevators that could obviate the need for rocket propulsion systems. However, the materials that would be required for these still do not possess the necessary properties.
Henning Krause from the division Communications and Media Relations from the Helmholtz Association answered this question.