If the module doesn't offer that possibility to configure it that way in Module Manager, maybe You can make a new Custom HTML module, fill it out how you want and make the text/image in that module link to the K2 category URL, which You have to find out beforehand.
EDIT: I just checked, under the modules configuration, there is even an option to change the "source of articles" to K2 Categories, i myself cannot verify this, because I uninstalled K2 completely, but maybe someone else can.
See attached image
Best Regards
Rain