  Full sky maps of energetic neutral atoms (ENA) obtained with the Interstellar
Boundary Explorer revealed a bright, arc-like Ribbon. We compare possible,
though as yet undetected, He ENA emission in two models of the Ribbon origin.
The models were originally developed for hydrogen ENA. In the first one, ENA
are produced outside the heliopause from the ionized neutral solar wind in the
direction where the local interstellar magnetic field is perpendicular to the
line-of-sight. The second model proposes production at the contact layer
between the Local Interstellar Cloud (LIC) and the Local Bubble (LB). The
models are redesigned to helium using relevant interactions between atoms and
ions. Resulting intensities are compared with possible emission of helium ENA
from the heliosheath. In the first model, the expected intensity is ~ 0.014
(cm^2 s sr keV)^-1, i.e., of the order of the He emission from the heliosheath,
whereas in the second, the LIC/LB contact layer model, the intensity is ~ (2-7)
(cm^2 s sr keV)^-1, i.e., a few hundred times larger. If the IBEX Ribbon needs
a source population of He ENA leaving the heliosphere, it should not be visible
in He ENA fluxes mainly because of the insufficient supply of the parent He ENA
originating from the neutralized solar wind {\alpha}-particles. We conclude
that full-sky measurements of He ENA could give promising prospect for probing
the Local Interstellar Medium at the distance of a few thousand AU and create
possibility of distinction between above mentioned models of Ribbon origin.
