  We construct off-shell recursion relations for arbitrary loop-level
scattering amplitudes beyond the conventional tree-level recursion relations
for $\phi^{4}$-theory and the Yang-Mills theory. We define a quantum
perturbiner expansion that includes loop corrections from the quantum effective
action formalism by identifying the external source. Our method clearly shows
how the perturbiner expansion becomes an off-shell current generating function.
Instead of using the classical equations of motion in the conventional
perturbiner method, we exploit the Dyson-Schwinger equation to derive the
quantum off-shell recursion relation to arbitrary order of loop-level
scattering amplitudes. We solve the recursion relation and reproduce the
results which agree up to one-loop six-point scattering amplitudes for
$\phi^{4}$-theory. Furthermore, we construct the recursions for computing
loop-level correlation functions by replacing the choice of the external
source.
