  We address the important issue of isotropisation of a pre-bounce contracting
phase in $f(R)$ gravity, which would be relevant to construct any viable
nonsingular bouncing scenario in $f(R)$ gravity. The main motivation behind
this work is to investigate whether the $f(R)$ gravity, by itself, can
isotropise a contracting universe starting initially with small anisotropy
without incorporating a super-stiff or non-ideal fluid, that is impossible in
general relativity. Considering Bianchi I cosmology and employing a dynamical
system analysis, we see that this is not possible for $R^n$ ($n>1$) and
$R+\alpha R^2$ ($\alpha>0$) theory, but possible for $\frac{1}{\alpha}e^{\alpha
R}$ ($\alpha>0$) theory. On the other hand, if one does not specify an $f(R)$
theory a priori but demands a cosmology smoothly connecting an ekpyrotic
contraction phase to a nonsingular bounce, the ekpyrotic phase \emph{may} not
fulfil the condition for isotropisation and physically viability
simultaneously.
