  In this article we explore the pre-inflationary background dynamics of an
FLRW universe sourced by a scalar field with monodromy potential in LQC
framework. In particular we calculate the number of e-folds, $N_{inf}$,
produced during the slowly rolling phase of the inflation and find out the
critical value of the ratio of the kinetic to potential energy, $r_w^c$, at the
quantum bounce that is required to produce $N_{inf}\simeq 60.$ Two different
monodromy potentials, namely, linear and quadratic with a modulation term are
investigated to this effect. The effects on the value of $N_{inf}$ due to
parameters associated with the strength, decay constant and the phase factor of
the modulation term are calculated. In addition to this we present the
qualitative picture of the background dynamics by carrying out a dynamical
system analysis. We produce the phase portraits and carry out a detailed linear
stability analysis of the finite fixed points, if any, for each of the
potentials.
