Putin cannot give him directly to America without the Russian stance losing credibility and they would look mercurial which would deter others using it as a safe haven. They've made plenty of hay out of Snowden's presence and would be loathe to lose possible future haymaking supplies.
Trump wouldn't know what to do with him if he had him. The Dems immediately take to the high horse and he loses the libertarians altogether. That loses him the balance of power with the social conservatives and that would be a problem for him getting re-elected because Sanders could easily turn him into George III.
The alternative is for Russia to get something big like formal recognition of Crimea (flying as Putin the magnificent horsetrader putting Russia first) and Snowden gets a quick trial with relatively short sentence of five-ten years and STFU good behavior policy thereafter.
I think the first scenario is the more likely so I think Snowden may receive an invitation to a nice European country such as Switzerland.