We consider in this article battery state of power (SoP) estimation, in particular, we propose two algorithms for predicting voltage corresponding to a future current profile that is known to be demanded by the battery load. The proposed algorithms belong to the class of data-driven methods and are based on the Gaussian Process Regression (GPR) framework. In comparison to conventional model-based approaches, datadriven approaches circumvent the issue of observability of SoP from measurements, especially pronounced in batteries with flat open circuit voltage (OCV) characteristic. In addition, the GPR framework admits accurate modeling of a fairly complicated battery dynamics using training data. Finally, the considered setup enables a relatively easy access to training data whenever the necessity for retraining arises, such as due to battery aging. The proposed algorithms aim to handle diverse battery operating conditions involving smooth and abruptly changing voltage/current measurements with both relatively small and large training datasets. The algorithms are tested on two such datasets, and the measured prediction performance and computation time verify their viability for real-time industrial use. We conclude with a number of possible directions for future research.