The Allies spent a fair amount of time considering how to deal with the Axis leadership, including Hitler, throughout much of the war, as detailed here, and in the end, despite voices to the contrary, the result was a commitment to legal proceedings.
The Nazis were not quite so thorough in their approach, and in fact there just isn't all that much to suggest the precise path things would have taken. Quick show trials were of course a possibility, but the final result would most certainly be preordained. In the Table Talk, Hitler speaks only quite briefly on the future death of Stalin, but it is also telling:
As regards the Russians, their powers of resistance are inimitable, as they proved in the Russo-Japanese War. This is no new characteristic which they have suddenly developed. If anything happens to Stalin, this great Asiatic country will collapse. As it was formed, so it will disintegrate. [...]
Here is a lesson we should do well to learn: if we do not complete the conquest of the East utterly and irrevocably, each successive generation will have war on its hands, in a greater or lesser degree. Even stupid races can accomplish something, given good leadership. Genghis Khan's genius for organisation was something quite unique.
What would that mean in practical terms? In the end we can only really speculate because the Germans didn't put in the effort to document just what they would do and prepare for trials after the war like the Allies and so on, which is what allows us to be more grounded in our assumptions about the reverse scenario for Hitler. But certainly it is clear enough that Hitler believed the Soviet Union was held together in no small part by the will of Stalin - at points in the Table Talk and elsewhere he even is oddly praiseful in ways - and that cutting off the head was the most assured way for the body to collapse.
Would that mean a show-trial and public execution? An anonymous death in a Gestapo basement? Consignment to a concentration camp where "nature" could take its course? Nothing I've read in the past suggests solid enough planning for us to pick one of those with certainty, although I can't be certain that there isn't some document out there overlooked by most sources which offer more hints. Of course, a reading of Stalin would suggest, I feel, that he would have followed Hitler's lead in the reverse scenario, dreading whatever his Nazi opponent might have in store for him, rendering such plans null in any case, but that again is something we can only speculate on by reading the broad scenario rather than real, specific evidence.
The closest thing we can use for real evidence though is simply the fate of those high ranking Soviet figures who were captured. To be sure, none had the stature of Stalin, to they present a shaky comparison at best, but nevertheless offer at least some insight into how the Nazis treated captured "Bolsheviks". Some, most famously Andrey Vlasov, were turned, Vlasov becoming the head of the Russian Liberation Army, a puppet force including white exiles and men recruited from POW camps who saw it as a better alternative, but others who remained loyal suffered greatly for their allegiance, as while Western soldiers captured could expect at least the semblance of proper treatment, in the East, Soviet captives were treated with absolute brutality right up to the top.
If anything, the leadership were the ones singled out for ill-treatment, the captors intent on "destroying the captured generals' remaining authority, both morally and physically." Some, like Vlasov, eventually broke and turned, while others resisted to the bitter end, a total of 20,000 Soviet officers of all ranks being killed in German hands. The best case scenario was being sent to rot in a POW camp or concentration camp, to die of illness such as V.I. Prokhorov, while others were tortured to death, such as the fate that befell A.D. Kuleshov, both of whom who had been held at Flossenburg Concentration Camp. Some were executed for their attempts to resist camp authorities, such as I. A. Presniakov. Executions continued right up to the end of the war, with D.M. Karbyshev hanged in February of '45, only after, it was reported, being brutally tortured. The sad irony is that barely any recognition of those who resisted was made by the Soviet authorities who saw all POWs as subject to suspicion for their true loyalty, however much they had suffered. It was only after Stalin's death that any effort of rehabilitation was made, and even then only for a small handful who had made exceptional efforts, such as G.I. Tkhor, who had organized a successful escape attempt for eleven officers that reached Soviet lines and could report on his efforts, for which he was hanged by the Germans.
Similarly, we can also look to Nazi policy as exemplified in the "Commissar Order", which encouraged the execution of captured political officers of the Red Army (a war crime, brought up at Nuremberg, it can be added). The language in justifying the order is startlingly similar to that used by Hitler in talking about the power of Stalin in keeping the Soviet Union fighting, noting:
That the originators of the asiatic-barbaric methods of fighting are the political commissars. They must be dealt with promptly and with the utmost severity.
The Nazis conceptualized it not as a normal war, but a clash of ideologies and a struggle for existence. Destroying "Bolshevism" down to the root was a key, central war aim, and the party itself was just as much an enemy - perhaps more, even - than the soldiers themselves.
The overall picture is essentially one of the systematic destruction of leadership and moral authority, not dissimilar to the Soviets' own approach to Eastern Poland from 1939-1941 where they set about murdering thousands of members of the Polish political and military elite. Stalin was the top of that tree, the felling of which was a Nazi priority, and while again, verbose planning for Stalin's specific fate might not be easy to find, we nevertheless can contextualize what would likely befall him both within the remarks of Hitler himself, and the broader treatment of Soviet leadership within German hands.
Sources
Directives for the Treatment of Political Commissars ("Commissar Order") (June 6, 1941)
Hitler, Adolf & Hugh Trevor-Roper. Hitler's Table Talk 1941-1944: Secret Conversations. Enigma Books, 2000.
Maslov, Aleksander A. Captured Soviet Generals: The Fate of Soviet Generals Captured by the Germans, 1941-1945. Psychology Press, 2001.
I would also note that as said above, this is in part sources just on a broader reading of the relevant literature, insofar as one can source a statement that is in the end "No one wrote much about this!"