  We provide a new approach towards the analysis of the fusion products defined
by B.~Feigin and S.~Loktev in the representation theory of (truncated) current
Lie algebras. We understand the fusion product as a degeneration using
Gr\"obner theory of non-commutative algebras and outline a strategy on how to
prove a conjecture about the defining relations for the fusion product of two
evaluation modules. We conclude with following this strategy for
$\mathfrak{sl}_2(\mathbb{C}[t]) $ and hence provide yet another proof for the
conjecture in this case.
