We study and constraint Mass-Varying Neutrino models using present and future available data .
In these models , dark energy is a self-interacting scalar field directly coupled to neutrinos .
We investigate two different potentials and both positive and negative coupling parameter \beta .
This corresponds to increasing or decreasing neutrino mass , respectively .
We explore couplings up to | \beta| \lesssim 5 .
In the case of the exponential potential , we find upper limits on \omega _ { \nu } < 0.004 at 2- \sigma level .
In the case of the inverse power law potential the null coupling can be excluded with more than 2- \sigma significance , the limits on the coupling being \beta > 3 for the increasing neutrino mass and \beta < -1.5 for the decreasing mass case .
This is a clear sign of a preference for higer couplings .
When including a prior on the neutrino mass today the upper limits on the coupling become | \beta| < 3 at 2- \sigma level for the exponential potential .
Finally , we present Fisher forecast using the tomographic weak lensing from the Euclid-like experiment , also in combination with the CMB temperature and polarization spectra from the Planck-like mission .
If considered alone , lensing data is very efficient in constraining \omega _ { \nu } , giving a signal of a non-null neutrino mass with high significance .
There is , however , a strong degeneracy in the \beta - \omega _ { \nu } plane .
When the two data sets are combined , the latter degeneracy remains , but the zero \beta value can be excluded at more than 2- \sigma .