O'Connell is yet to feature in the RaboDirect PRO12 this season - although he did appear in the Heineken Cup - and Kearney does not know when he will be ready for action.
"It's out there that he's had a couple of injections," Kearney told the Irish Independent. "He had a further injection on Friday. That's all the detail I can give at this stage. He has a bulging disc in his back.
"It will be managed for the next while and the hope is that it can settle down over the next few weeks.
"He had the injury before he came into the squad and it settled down well. The nature of the injury means that it's a question of wait and see.
"It isn't a black and white situation in terms of knowing the exact prognosis for what you do from this moment on.
"I'm sure there is a time limit but that will be decided between Paul and the specialists who are treating him."