  The $\eta$ mesic nucleus is considered to be one of the interesting exotic
many body systems and has been studied since 1980's theoretically and
experimentally. Recently, the formation of the $\eta$ mesic nucleus in the
fusion reactions of the light nuclei such as $d + d \rightarrow (\eta + \alpha)
\rightarrow X$ has been proposed and the experiments have been performed by
WASA-at-COSY. We develop a theoretical model to evaluate the formation rate of
the $\eta$ mesic nucleus in the fusion reactions and show the calculated
results. We find that the $\eta$ bound states could be observed in the
reactions in cases with the strong attractive and small absorptive
$\eta$-nucleus interactions. We compare our results with existing data of the
$d + d \rightarrow \eta + \alpha$ and the $d + d \rightarrow {^3 \rm He} + N +
\pi$ reactions. We find that the analyses by our theoretical model with the
existing data can provide new information on the $\eta$-nucleus interaction.
