Alexander was (at least ostensibly) supportive of Eugene, same as he apparently made some promises to Murat too: when it came the moment of drawing lines on the map of Europe the idealistic Alexander became again a hard-lined defender of immediate Russian interests.Wasn't Alexander I in favour of Eugene or the de Beaharnaises getting something otu of it? I seem to recall Metternich also offered him something if he'd drop Napoléon (through his father-in-law). But then again, I'd count my fingers after shaking hands with either. How serious both were (Alexander was for Louis Philippe or Bernadotte becoming ruler of France, and Metternich was in favour of the king of Rome) is obviously relative, though
IIRC, Eugene's father in law urged him to distance himself from Napoleon at the end of 1813, beginning 1814. It may well has been because Metternich pushed him to do it, but there was never a mention of what Eugene could have kept. The kingdom of Italy was out of the question, since the strategic goal of Austria was to become the dominant power in Italy. Maybe a principality in Romagna, with possibly the addition of Bologna (the other papal legation, Ferrara, would go to Austria in such a case): it would have meant that the Papal States would not have been reconstituted, or at least would have been pruned down to Latium only. While the end to the temporal power of the pope was considered, in the end the Powers refrained from doing so: Metternich himself regretted this decision during the 1830s when it became clear that the awful government of the Papal States could not and would not be reformed.
The other alternative would have been a two-penny crown in the Germanies, but I doubt very much Eugene would have considered such an offer. In the end anyway the necessary condition was a betrayal of Napoleon in January-February 1814, with Eugene throwing himself to the dubious mercy of the Coalition Powers, and this was not a move that Eugene was willing to consider either.