Could Twitter soon go head-to-head with WhatsApp, Kik and other big mobile messaging services? Unnamed sources tell AllThingsD that Twitter has been working on “plans to significantly update its direct-messaging product in the near future” and has even “kicked around the idea of launching a standalone direct-messaging application separate from the Twitter app.” Doing a standalone direct-messaging app would put Twitter in direct competition with the scores of messaging apps that have taken the mobile world by storm over the past couple of years. AllThingsD notes that Twitter is still not settled as to whether its messaging revamp will include a standalone app for direct messages, although the company is definitely feeling some competitive heat from its rivals in the mobile messaging world.