  Within a simple Ansatz for renormalized gluon propagator and using gauge
invariant pinch-technique for Schwinger-Dyson equation, the limits on the
effective gluon mass is derived. We calculated scheme invariant running
coupling, which in order to be well defined, gives the lower limit on the gluon
mass. We conclude mass should be larger as $m>0.4\Lambda$ in order to avoid
Landau ghost. The upper limit is estimated from assumed quark mass generation
which requires gauge coupling must be large enough to trigger chiral symmetry
breaking. It allows only small range of $m$, which lead to a reasonably large
infrared coupling. Already for $m\simeq \Lambda$ we get no chiral symmetry
breaking at all. Further, we observe that sometimes assumed or postulated
Khallen-Lehmann representation for running coupling is not achieved for any
value of $m$.
