Following the announcement of a new period of activity of the soft gamma-ray repeater SGR 1806-20 in 1996 November, we have performed follow-up observations of the IR counterpart, which has been proposed as a luminous blue variable or B[e] star. We have found that no variability larger than 0.1 mag in the K-band is present in the data. No variation in the K-band flux is found either when comparing our observations (1996 November 6 & 10) with a previous one (1996 July 3), nor any variation larger than 0.1 mag was detected in the K-band on 6 November at the 1-second timescale. Assuming that a faint burst (with fluence S ~ 10(-9) erg cm(-2) ) occurred during our observation, we can set an upper limit to the fluences rate (assuming a 1-s IR burst) as S_IR ({sl K-band)}/S_{gamma (25-130 keV)} <= 10(-2) . There is a modest chance that no burst at all could have occurred during our observation. In that case the upper limit quoted here is considerably worse. Photometry revealed that the HK magnitudes are consistent with the values reported by Kulkarni etal. (1995) in 1993 October, but the J value is slightly different by about 0.4 mag. Based on observations made with the Carlos Sánchez Telescope operated on the island of Tenerife in the Spanish Observatorio del Teide of the Instituto de Astrof\'{i