  The possibility of an $nn\Lambda$ bound state is investigated in the
framework of pionless effective field theory at leading order. A system of
coupled integral equations are constructed in the spin-isospin basis, of which
numerical solutions are investigated. In particular, we make use of the limit
cycle behavior, i.e., cyclic singularities of coupled integral equations of the
system, which would be associated with the formation of a three-body bound
state, so-called the Efimov state, in the unitary limit. Furthermore, we find
that, when the sharp momentum cutoff introduced in the integral equations is
taken significantly larger than the hard scale of the effective theory, the
coupling of a three-body contact interaction becomes cyclically singular
indicating the onset of Efimov-like bound state formation. However, the paucity
of empirical information to determine the parameters of the theory precludes a
definitive conclusion on the existence of such a bound state. As a simple test
of the feasibility of the $nn\Lambda$ bound system in nature, we explore the
cutoff dependence of the theory, and uncertainties of the present study are
discussed as well.
