With their smarts and unique appearance, octopuses are marine aquarium favorites. Here are some facts you need to know before bringing home an eight-legged friend.
To answer your question, yes, it is possible. As mentioned, however, it would likely require a specialized setup.
Blaxsun’s link above is a great place to start if you’re seriously considering an octopus tank. If, after you’ve read through that article, you decide that an octopus is right for you, I would recommend heading over to Tonmo (a forum site similar to Reef2Reef but specifically dedicated to cephalopods like octopus, squids, cuttlefish, etc.) and reading through the info available there about the specific species you’re hoping to keep. They have info available for most of the species commonly available in the hobby.
If your goal is specifically to breed the octopus, then I just have to warn you that there are “large egg” octopus species and “small egg” octopus species- currently, the large egg species can be kept and bred, and you can rear the young in captivity. Unfortunately, the same cannot be said for the small egg species. While you can keep and breed the small egg species in captivity, no one has successfully reared the young yet. As I understand it, the most successful attempts in recent years (which were not successful by any means - none of the young octopus survived) have utilized live crab zoea (baby crabs) as the food. Normal breeder foods won’t cut it, and the foods they’re trying now are expensive and extremely difficult to come by. So, if you’re hoping to breed them, I would verify that it’s a large egg species in advance.