That seems to be what members of Jackson's City Council are proposing in this WAPT News Report. Councilwoman Larita Cooper-Stokes recommends a policy that would require "everyone who's using drones in the City of Jackson" to register, noting that "we need to know who you are and we need to know what you're doing." Councilman De'Keither Stamps points out that privacy concerns are motivating the call for restriction, and worries about the prospect of people using drones to look through other people's windows.
The Clarion-Ledger reports on the story here, and notes that other cities have restricted the use of drones. This includes Iowa City, which banned the use of police drones last summer. A universal licensing requirement, however, would not be limited to government drones -- it would affect everybody.
While drones may be used to spy on people in ways that alternative technology could not facilitate, I think that calls for a drone registry are alarmist. Gregory McNeal argues that a lot of journalism about drones is "sensational," but that many of these reports end up covering incidents where the drone use was far more benign than initially reported. For example, a Seattle woman claimed that a drone had been spying on her through her window, and this caught the attention of the media. But it turned out that the drone was only being used to survey a site for a new building.
I also think that Cooper-Stoke's vague description of drone registration was concerning, namely that she wants to know what people are doing with their drones. It is not clear to me what sort of information would be collected by this registration scheme, and it is also unclear how this would help prevent the invasive use of drones.
While I am all for clearer regulation of drone technology, I think that the danger of private drones invading people's privacy is currently fairly low. Universal registration is far too blunt of an instrument to address the complicated question of regulating drones.