The He I λ10833 Å triplet is a powerful tool for characterising the upper atmosphere of exoplanets and tracing possible mass loss. Here, we analysed one transit of GJ 1214 b observed with the CARMENES high-resolution spectrograph to study its atmosphere via transmission spectroscopy around the He I triplet. Although previous studies using lower resolution instruments have reported non-detections of He I in the atmosphere of GJ 1214 b, we report here the first potential detection. We reconcile the conflicting results arguing that previous transit observations did not present good opportunities for the detection of He I, due to telluric H₂O absorption and OH emission contamination. We simulated those earlier observations, and show evidence that the planetary signal was contaminated. From our single non-telluric-contaminated transit, we determined an excess absorption of 2.10_−0.50^+0.45% (4.6 σ) with a full width at half maximum (FWHM) of 1.30_−0.25^+0.30 Å. The detection of He I is statistically significant at the 4.6 σ level, but repeatability of the detection could not be confirmed due to the availability of only one transit. By applying a hydrodynamical model and assuming an H/He composition of 98/2, we found that GJ 1214 b would undergo hydrodynamic escape in the photon-limited regime, losing its primary atmosphere with a mass-loss rate of (1.5–18) × 10¹⁰ g s⁻¹ and an outflow temperature in the range of 2900–4400 K. Further high-resolution follow-up observations of GJ 1214 b are needed to confirm and fully characterise the detection of an extended atmosphere surrounding GJ 1214 b. If confirmed, this would be strong evidence that this planet has a primordial atmosphere accreted from the original planetary nebula. 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.