On 28 May 2008, the Swift satellite detected the first reactivation of SGR 1627-41 since its discovery in 1998. Following this event we began an observing campaign in near infrared wavelengths to search for a possible counterpart inside the error circle of this SGR, which is expected to show flaring activity simultaneous to the high energy flares or at least some variability as compared to the quiescent state. For the follow-up we used the 0.6m REM robotic telescope at La Silla Observatory, which allowed a fast response within 24 hours and, through director discretionary time, the 8.2m Very Large Telescope at Paranal Observatory. There, we observed with NACO to produce high angular resolution imaging with the aid of adaptive optics. These observations represent the fastest near infrared observations after an activation of this SGR and the deepest and highest spatial resolution observations of the Chandra error circle. 5 sources are detected in the immediate vicinity of the most precise X-ray localisation of this source. For 4 of them we do not detect variability, although the X-ray counterpart experimented a significant decay during our observation period. The 5th source is only detected in one epoch, where we have the best image quality, so no variability constrains can be imposed and remains as the only plausible counterpart. We can impose a limit of Ks > 21.6 magnitudes to any other counterpart candidate one week after the onset of the activity. Our adaptive optics imaging, with a resolution of 0.2 provides a reference frame for subsequent studies of future periods of activity.