Context. Synchrotron radio halos at the center of merging galaxy clusters provide the most spectacular and direct evidence of the presence of relativistic particles and magnetic fields associated with the intracluster medium. The study of polarized emission from radio halos has been shown to be extremely important to constrain the properties of intracluster magnetic fields. However, detecting this polarized signal is a very hard task with the current radio facilities. Aims: We investigate whether future radio observatories, such as the Square Kilometer Array (SKA), its precursors and its pathfinders, will be able to detect the polarized emission of radio halos in galaxy clusters. Methods: On the basis of cosmological magnetohydrodynamical simulations with initial magnetic fields injected by active galactic nuclei, we predict the expected radio halo polarized signal at 1.4 GHz. We compare these expectations with the limits of current radio facilities and explore the potential of the upcoming radio interferometers to investigate intracluster magnetic fields through the detection of polarized emission from radio halos. Results: The resolution and sensitivity values that are expected to be obtained in future sky surveys performed at 1.4 GHz using the SKA precursors and pathfinders (like APERTIF and ASKAP) are very promising for the detection of the polarized emission of the most powerful (L1.4 GHz > 1025 Watt/Hz) radio halos. Furthermore, the JVLA have the potential to already detect polarized emission from strong radio halos, at a relatively low resolution. However, the possibility of detecting the polarized signal in fainter radio halos (L1.4 GHz ≃ 1024 Watt/Hz) at high resolution requires a sensitivity reachable only with SKA.