In 2004, the DLR commissioned a study into possible future routes called "Horizon 2020". They seem to have quietly forgotten about it, at least publicly, but I spotted a mention of the results in this Hackney Council report:
Three schemes remain under review in spring 2006. These are Bank – Farringdon, Bank – Liverpool Street – Shoreditch (Bishopsgate Goodsyard site), and Bank – Charing Cross.The Charing Cross scheme has been widely discussed and even appears on one of the Crossrail maps. The other two are complete news to me. The route to Farringdon would surely involve the abandoned Thameslink tracks from Moorgate, and the route to Liverpool St would be a logical extension of the overrun tunnel that already points northeast.
[Update: A commenter prompted me to check where the Bank overrun tunnel goes. Although at least one diagram shows it heading for Liverpool Street, I've found several credible sources suggesting it heads northwest torwards Moorgate. My mistake. ]
Of course I have no idea if any of these are still being considered, but it's interesting to know they were at one point.