Modifications of dynamical and thermodynamical behavior of liquids in confinement are of the uttermost importance. Many liquids are confined in systems of interest for both technological applications and biology. Very few computer simulations on the study of the glass transition scenario in confined liquids are available. We present an extensive study upon cooling on the behavior of a model glass former, a liquid Lennard Jones binary mixture, confined in a model for xerogels. Modification of the dynamical and thermodynamical behavior on approaching the glass transition with respect to the bulk are studied in detail. In particular a test of the Mode Coupling predictions is performed with respect to the bulk behavior and upon varying the host confining medium characteristics. A study of the thermodynamic behavior via inherent structure analysis is also performed. The Mode Copuling Theory appears to be able to account for the behaviour of the liquid mixture also in confinement, but with important modification of the parameters of the theory with respect to the bulk. The mode coupling crossover temperature and the Kauzman temperature are evaluated. Both appear to occur at lower temperatures with respect to the bulk. The possible effect of confinement on dynamical heterogeneities is also discussed for this model.The results can help to shed light on the influence of this important feature on the glass transition.