Internal contaminations of ²³⁸U, ²³⁵U and ²³²Th in the bulk of high purity germanium detectors are potential backgrounds for experiments searching for neutrinoless double beta decay of ⁷⁶Ge. The data from GERDA Phase I have been analyzed for alpha events from the decay chain of these contaminations by looking for full decay chains and for time correlations between successive decays in the same detector. No candidate events for a full chain have been found. Upper limits on the activities in the range of a few nBq/kg for ²²⁶Ra, ²²⁷Ac and ²²⁸Th, the long-lived daughter nuclides of ²³⁸U, ²³⁵U and ²³²Th, respectively, have been derived. With these upper limits a background index in the energy region of interest from ²²⁶Ra and ²²⁸Th contamination is estimated which satisfies the prerequisites of a future ton scale germanium double beta decay experiment.