Some kind of union, maybe, but Soviet?!
Apparently the "soviet" form of government is based on government by a central council. E.g. instead of a mayor, a soviet-governed city would have a city council, and perhaps a city manager that executed the council's will.
So a soviet-style system of subordinate governments seems like a reasonable goal for Putin to have. Another reasonable possibility would be a more "strongman"-based system, with subordinate governments being given to loyal henchmen to rule over (and profit from). But there are drawbacks to the strongman approach:
Dissatisfaction of the masses, who will likely prefer some kind of democratic voice in their local government. A council of elected officials helps to keep the governed happy and compliant.
Reliability of loyal henchmen. A council dilutes individual power and creates some checks and balances on individual corruption and ambition.
Scalability. The more henchmen you have running things on your behalf, the more people you have to personally supervise and watch out for. A council of elected officials is going to be too busy running for office and pleasing their constituents to plot betrayal, as well as watching each other closely for signs of growing advantage.
So some kind of soviet union, maybe, but Socialist?!