We consider the possibility to gain information on the lepton mixing matrix element | U e 3 | from an improved experimental limit on the effective neutrino mass governing neutrinoless double beta decay. We show that typically a lower limit on | U e 3 | as a function of the smallest neutrino mass can be set. Furthermore, we give the values of the sum of neutrino masses and | U e 3 | which are allowed and forbidden by an experimental upper limit on the effective mass. Alternative explanations for neutrinoless double beta decay, Dirac neutrinos or unexplained cosmological features would be required if future measurements showed that the values lie in the respective regions. Moreover, we show that a measurement of | U e 3 | from neutrinoless double beta decay is very difficult due to the expected errors on the effective mass and the oscillation parameters.