Yes, if they have different streams of consciousness, as a number of philosophical theologians have proposed.
By illustration, someone with fragmented personalities could "know" something in one personality but not in the other. Now some writers, notably Thomas Morris and Richard Swinburne, have suggested that Christ could have had a split mind in a somewhat analogous way. His divine stream of consciousness would have carried on as before, complete with its omniscient knowledge. But he would have had a human stream of consciousness parallel with it, which would not have had omniscient knowledge. In such a case, Christ would have been omniscient (in virtue of his divine consciousness), but in his human consciousness he would not have had access to that knowledge and might not even have known that he had it.
Remember that, historically, theologians have held that Christ had two minds - a human one and a divine one. This is because it was thought that, if he hadn't had a distinct human mind in addition to his divine mind, he would not have been truly human. So the Morris/Swinburne idea of the split mind is really just a modern restatement. The difference is that, classically, Christian theologians have thought that even the human mind was omniscient, on the grounds that although it was human, it must have been perfect, and therefore have had all knowledge (and any other perfections) that a human mind is capable of. Modern philosophical theologians tend not to think this, and those who posit the two-mind or split-mind theory suppose instead that, while the divine mind is omniscient, the human mind is not.
