If I recall correctly, he had been prepared to dedicate a piece to him, but then changed his mind after Napoleon became essentially a dictator. Why did Beethoven like Napoleon to begin with, though? What about the man appealed to him?
The attraction to Napoleon was in no small measure due to the fact that Napoleon seemed to embody both the Romantic ideal of the individual triumphing over adversity and values of the Enlightenment in which reason and order triumphed over chaotic superstition. Napoleon's own biography as a provincial minor noble who eventually became the master of Europe mirrored the Romantics' preoccupation with the power of the will and the individual. The structure of the Consulate with its precise delineations of power and strong executive dovetailed with the authoritarian strains of Enlightenment thought that supposed man should be governed by apolitical intellectuals. Both the Enlightenment and Romantic ideals complimented each other, Napoleon was First Consul not only because he was the most rational choice, but also because he took control over his own destiny. Of course, Napoleon himself cultivated this bifurcated image and his nascent propaganda embellished his unique genius in his ascent to power.
This fusion of reason and genius in the figure of one man was very attractive to many intellectuals of the period and since. After Goethe met Napoleon in Erfurt in 1808, the German poet is reported to have said "that man, he is the distillation of the world!" Beethoven himself oscillated between dislike and admiration for Napoleon that continued throughout his life. The diary of Baron de Trémont in 1809 recorded a conversation with Beethoven in which "the greatness of Napoleon preoccupied [Beethoven] and he often spoke to me about it. I observed, he admired Napoleon's ascent from such a low beginning. It suited his democratic ideas." De Trémont further elaborated that part of Beethoven's problem with Napoleon was that he failed to live up to Napoleon's own symbolism as a transgressive figure. In an April 1802 letter, he noted that he would not create a sonata for the French Revolution because "everything is starting to slip back into the old rut, now that Bonaparte has concluded his Concordat with the Pope." The allure of Napoleon stayed with Beethoven and many intellectuals well past Waterloo; few of his contemporaries could command such attention or were as charismatic. Beethoven's response to news of Sir Walter Scott's Romantic biography Life of Napoleon in 1824 was "Napoleon! Formerly I disliked him. Now I think quite differently."