I'm fairly sure that offline in the expression "let's take it offline" arises from the sense that offline has in the context of company data networks. From Dan Balter, Managing and Maintaining a Windows Server 2003 Environment (2003):
You can mount and dismount volumes from the command line with the mountvol.exe command. On basic disks, if you type mountvol x: /p, where x: represents the volume's drive letter, you can dismount a volume and take it offline. ... By removing the drive letter and any other paths (mount points) for the volume, you take the volume offline.
But in addition to taking server volumes offline (that is, off the shared network), you can (if you have the necessary level of administrative rights) take a specific file offline (by transferring the file to a specific hard drive and then deleting it from the shared network). Taking a conversation offline is metaphorically very similar to taking a file that was begun "online" (that is, on the shared network) and moving it offline (that is, to a more private destination).
The earliest mention of "take [it] offline" that I've been able to find is in Eric Raymond, The New Hacker's Dictionary (1996):
offline adv. Not now or not here. "Let's take this discussion offline." Specifically used on Usenet to suggest that a discussion be moved off a public newsgroup to email.