The structural transition occurring in droplets of nematic liquid crystals formed in a polymer in magnetic field is studied. The transition is caused by field-driven weakening of tangential surface anchoring and develops following two scenarios: bipolar structure/homogeneous structure or bipolar structure/radial structure. The first scenario suggests a cyclic transition occurring upon thermal fluctuations without field. The structural transition is considered within a model of the biaxial liquid crystal/polymer interface. The model describes tendency of the nematic director to align tangentially on a droplet's surface, normally under the action of flexoelectric polarization, and axially along the magnetic-field-imposed easy orientation axis.