  Considering a general mass matrix for quasi-degenerate neutrinos and treating
the experimentally known oscillation parameters as inputs, we study the
correlation between the degenerate mass scale $(m)$ and the mixing angle
$\theta_{13}$. We find that, corresponding to different values of $m$, there
exist upper bounds on $\theta_{13}$, so that a precise determination of the
latter in future may put upper limit on the former, and vice versa. One can
also find a possible correlation between $m$ and lower bound of $\theta_{13}$,
depending on the relative strength of the unperturbed degenerate mass matrix
and the perturbation. The possible constraints on the parameters of few models
of quasi-degenerate neutrinos are briefly discussed.
