Napoleon is actually drunk. I believe this actually happens in the end of chapter 7.
Squealer comes out of the house reporting Napoleon is dying, but he is really dealing with a hang over. As the day progresses, Napoleon recovers more and more.
Pages after this situation we learn that one of the commandments has again changed:
No animal shall drink alcohol to excess.
Napoleon has learned from alcohol's effects and has also ruled that anyone who does drink to excess will be put to death.
This is in Chapter 8, towards the end.
I do not think it is clear that Napoleon actually thinks he is dying, but whether he does or not, what's really going on is that he is drunk.
The pigs find a case of whiskey in the cellar. Then Napoleon starts running around acting funny. Then they think he is dying. After that, Squealer comes out and announces that no one should drink alcohol.
Put that all together and it implies to me that Napoleon was drunk, even if they do claim that he has been poisoned by Snowball.
This question is slightly misleading in that Napoleon never says that he is dying. It is implied. Squealer is actually the one who tells the pigs that Napoleon is dying. The real reason for this is also implied. In chapter eight, it says that the pigs came upon a case of whisky. The following narrative says it all.
According to this narrative, there was the sound of loud singing from the farmhouse. However, the singing was mixed up. Also Napoleon was wearing an old bowler hat of Mr. Jones. And when Squealer was seen in the morning, he was walking slowly and his tail was lagging behind him. All the signs of drunkenness were present. This was when Squealer stated that Napoleon was dying. It was Napoleon's first experience with drunkenness. He had a hangover after a night of drinking.