Context :

Aims : We aim to explore the photosphere of the very cool late-type star VX Sgr and in particular the existence and characterization of molecular layers above the continuum forming photosphere .

Methods : We obtained interferometric observations with the VLTI/AMBER interferometer using the fringe tracker FINITO in the spectral domain 1.45-2.50 \mu m with a spectral resolution of \approx 35 and baselines ranging from 15 to 88 meters .
We perform independent image reconstruction for different wavelength bins and fit the interferometric data with a geometrical toy model .
We also compare the data to 1D dynamical models of Miras atmosphere and to 3D hydrodynamical simulations of red supergiant ( RSG ) and asymptotic giant branch ( AGB ) stars .

Results : Reconstructed images and visibilities show a strong wavelength dependence .
The H-band images display two bright spots whose positions are confirmed by the geometrical toy model .
The inhomogeneities are qualitatively predicted by 3D simulations .
At \approx 2.00 \mu m and in the region 2.35 - 2.50 \mu m , the photosphere appears extended and the radius is larger than in the H band .
In this spectral region , the geometrical toy model locates a third bright spot outside the photosphere that can be a feature of the molecular layers .
The wavelength dependence of the visibility can be qualitatively explained by 1D dynamical models of Mira atmospheres .
The best-fitting photospheric models show a good match with the observed visibilities and give a photospheric diameter of \Theta = 8.82 \pm 0.50 mas .
The H _ { 2 } O molecule seems to be the dominant absorber in the molecular layers .

Conclusions : We show that the atmosphere of VX Sgr rather resembles Mira/AGB star model atmospheres than RSG model atmsopheres .
In particular , we see molecular ( water ) layers that are typical for Mira stars .