  We consider, in a completely model-independent way, the transfer of energy
between the components of the dark energy sector consisting of the cosmological
constant (CC) and that of relic neutrinos. We show that such a cosmological
setup may promote neutrinos to mass-varying particles, thus resembling a
recently proposed scenario of Fardon, Nelson, and Weiner (FNW), but now without
introducing any acceleronlike scalar fields. Although a formal similarity of
the FNW scenario with the variable CC one can be easily established, one
nevertheless finds different laws for neutrino mass variation in each scenario.
We show that as long as the neutrino number density dilutes canonically, only a
very slow variation of the neutrino mass is possible. For neutrino masses to
vary significantly (as in the FNW scenario), a considerable deviation from the
canonical dilution of the neutrino number density is also needed. We note that
the present `coincidence' between the dark energy density and the neutrino
energy density can be obtained in our scenario even for static neutrino masses.
