A spin-off manga has started in this month's issue of Kodansha's shoujo magazine Aria. Its title is
K - Memory of Red, drawn by newcomer mangaka Kuroe Yui, and from what I gather, it's going to have Mikoto as its lead character and will mostly follow his gang's adventures, not necessarily related to the anime's other main characters. (Edit: Oh, it's actually a prequel, going by what the official Twitter has to say.)
For the record, the magazine does publish a few fujoshi-friendly titles such as No. 6. Not that it really means anything, what with many series getting various manga adaptations catering to different demographics lately... but the information's been so scarce up to this point that I'll take everything I can get.