Because a crossover between two liquid phases of water should manifest itself in a change of the dynamical behavior, we study the temperature-dependent motion of water in nanopores by nuclear magnetic resonance and broadband dielectric spectroscopy. Our results show that confined water exhibits a dynamical crossover at ca. 220 K, which is largely independent of the pore size. Further studies are required to determine to what degree this finding can be taken as evidence for the existence of a liquid-liquid phase transition. In particular, it is necessary to analyze whether the dynamical crossover is related to the properties of bulk water or caused by the severe confinement.