The He I λ10833 Å triplet is a powerful tool for characterising the upper atmosphere of exoplanets and to trace possible mass losses. We analysed one transit of GJ 1214b observed with the CARMENES high-resolution spectrograph to study its atmosphere via transmission spectroscopy around the He I triplet. Despite previous intensive observations from space- and ground-based observatories, our He I excess absorption is the first tentative detection of a chemical species in the atmosphere of this benchmark sub-Neptune planet. We reconcile the conflicting results arguing that previous transit observations did not present good opportunities for the detection of He I, due to telluric water absorption and OH emission contamination. Further high-resolution follow-up observations of GJ 1214b are needed to confirm and fully characterise the detection of an extended atmosphere surrounding GJ 1214b. If confirmed, this would be strong evidence that this planet has a primordial atmosphere accreted from the original planetary nebula.