  For a finite group $G$ and subset $S$ of $G,$ the Haar graph $H(G,S)$ is a
bipartite regular graph, defined as a regular $G$-cover of a dipole with $|S|$
parallel arcs labelled by elements of $S$. If $G$ is an abelian group, then
$H(G,S)$ is well-known to be a Cayley graph; however, there are examples of
non-abelian groups $G$ and subsets $S$ when this is not the case. In this paper
we address the problem of classifying finite non-abelian groups $G$ with the
property that every Haar graph $H(G,S)$ is a Cayley graph. An equivalent
condition for $H(G,S)$ to be a Cayley graph of a group containing $G$ is
derived in terms of $G, S$ and $\mathrm{Aut }G$. It is also shown that the
dihedral groups, which are solutions to the above problem, are
$\mathbb{Z}_2^2,D_3,D_4$ and $D_{5}$.
