Well for the sake of giving a good answer to an interesting question: oddly enough, I'd say yes.
Influenza viruses attack our bodies by attaching to the specific cells of our mucous tissue. This type of tissue is in the lining of the respiratory system and also in the lining of the gastrointestinal system. So, it is possible to catch the flu if the virus gets on your mucous tissue regardless of where it is in your body.
So, since the rectum is also lined with this type of tissue, it is possible (although unlikely) for a virus particle to enter into your gastrointestinal system at the top and not attach to the mucous tissue cells until it gets to the bottom and then manages to attach to one before it is excreted. In that sense, you would have flu virus particles attached to the cells of your mucous tissue in your rectum. And that could be considered having flu in your rectum.
Alternately, if you had the virus on your hand (or an object) and if that managed somehow to touch the mucous tissue at your anus, then virus particles could be introduced and attach directly to the mucous tissue of the rectum near the anus, and then you could also have flu in your rectum.
The symptoms would still be of the respiratory flu, not the "stomach flu" (gastroenteritis), however. It is the kind of virus that determines the symptoms, not the location of the introduction of the virus.
the rectum
the rectum is attractive
The large intestine does connect to the rectum.
The rectum.the rectum or the decending colon.
Nothing is digested in the rectum, the rectum is the final storage place for feces before they are excreted.
Cancer of the rectum is the disease characterized by the development of malignant cells in the lining or epithelium of the rectum
it contract the rectum
The rectum is at the end of the large intestine.
At the base of the rectum starts the anus.
The anus is distal to the rectum.
Faeces (poo) is stored in the Rectum
what is erythematous mucosa in the distal rectum