Districts have to have equal numbers of people. One man one vote. They can’t move districts to thecities.
No, they could not simply ‘move’ districts to the cities. What they could do, however, is rearrange the districts so that there are a whole bunch of districts that have both urban and suburban (maybe rural, too) parts. In states controlled by Dems, these districts may be set up in such a way that they have populations that are 60-40 urban-nonurban. The opposite in states controlled by the GOP.