No, Norton 360 can't be used in Linux. Please check the System Requirements provided in the following link:
Currently, none of the consumer products (except PCanywhere) are supported in Linux. Enterprise products like Symantec AntiVirus and Enterprise Security Suite can be used in Linux. If you can post the same in the forum for Symantec Business Products, you may get more feedback.
If you are experiencing an issue that needs urgent assistance please visit our customer support area:
There are currently 6 users online.