  Despite about a decade of observations, very little is known about the
optical and infrared (IR) emission properties of the Soft Gamma-ray Repeaters
(SGRs) and of the Anomalous X-ray Pulsars (AXPs), the magnetar candidates, and
about the physical processes which drive their emission at these wavelengths.
This is mainly due to the limited number of identifications achieved so far,
five in total, and to the sparse spectral coverage obtained from multi-band
optical/IR photometry. Aim of this work is to search for a likely candidate
counterpart to the recently discovered transient radio AXP 1E 1547.0-5408. We
performed the first deep near-IR (NIR) observations (Ks band) of 1E 1547.0-5408
with the VLT on three nights (July 8th, 12th, and August 17th), after the X-ray
source rebrightening and during the subsequent decay reported around June 2007.
We detected four objects within, or close to, the 3sigma radio position of 1E
1547.0-5408. The faintest of them (object 1) has a brightness K = 20.27 +/-
0.05, which would yield an unabsorbed X-ray to NIR flux ratio FX/FKs ~ 800 for
1E 1547.0-5408, i.e. on average lower than those derived for other magnetars.
The non-detection of object 1 on the nights of July 8th and August 17th only
allowed us to set an upper limit of Delta Ks ~ 0.2 on its NIR variability,
which prevented us to search for correlations with the radio or X-ray flux. We
detected no other object at the radio position down to a limit of Ks ~ 21.7 (at
5sigma), computed in our deepest VLT image (July 12th). From our observations
we can not confidently propose a NIR counterpart to 1E 1547.0-5408. More NIR
observations of object 1, e.g. to determine its colors and to monitor
variability, would be conclusive to determine whether or not it can be
considered a plausible candidate.
