  A cosmological scenario where dark matter interacts with a variable vacuum
energy for a spatially flat Friedmann-Robertson-Walker space-time is proposed
and analysed to show that with a linear equation of state and a particular
interaction in the dark sector it is possible to get a model of an Emergent
Universe. In addition, the viability of two particular models is studied by
taking into account recent observations. The updated observational Hubble data
and the JLA supernovae data are used in order to constraint the cosmological
parameters of the models and estimate the amount of dark energy in the
radiation era. It is shown that the two models fulfil the severe bounds of
$\Omega_{x}(z\simeq 1100)<0.009$ at the $2\sigma$ level of Planck.
