I agree with others there is no real appetite for monarchy in Russia, although along with the revival in Orthodoxy there is greater interest in the Romanov dynasty than ever before. Russians are rediscovering their pre-1917 history and finding it isn't all terrible.
One of the main problems of course is there isn't an agreed candidate, although all those capable of understanding Romanov house law agree that Grand Duchess Maria and her son are the only living Romanov dynasts, there are others who pretend to be dynasts and cause dissension and confusion, which doesn't help the monarchist cause.
What you really need though is a Franco type figure who decides that Russia will be a monarchy again, either because he is traditionalist or simply because it will be a comfortable public front for a dictatorship.
At various times there have been rumours that Putin has toyed with introducing a monarchy, to be a focus for nationalism, he's probably the only one capable of doing it.
A lot of the renewed interest in the Imperial period is happening because the 400th Anniversary of the Romanov Dynasty was in 2013 so that also helped spur a reinvigorated interest in the Tsarist Era. Really, the internal disputes of the Romanov claimants are just the tip of the iceberg to the actual challenges to a restoration.
Frankly, I don't think anyone, least of all Putin, is going to toy with a restoration of the monarchy. It's really hard to overestimate his popularity in Russia. He's very successfully created a stable system yet one in which he has few real threats. Toying with actions like out-of-the-blue monarchical restorations is the game of either desperate leaders with waning popularity engaging in political theater to hold power, or hardline traditionalists who are firmly of the belief that the old ways are the best ways.
Putin is neither.