  The recent observation of the shadow of the supermassive compact object
M87$^*$ by the Event Horizon Telescope (EHT) collaboration has opened up a new
window to probe the strong gravity regime. In this paper, we study shadows cast
by two viable alternatives to the Kerr black hole, and compare them with the
shadow of M87$^{*}$. The first alternative is a horizonless compact object
(HCO) having radius $r_0$ and exterior Kerr geometry. The second one is a
rotating generalisation of the recently obtained one parameter ($r_0$) static
metric by Simpson and Visser. This latter metric, constructed by using the
Newman-Janis algorithm, is a special case of a parametrised rotating non-Kerr
geometry obtained by Johannsen. Here, we constrain the parameter $r_0$ of these
alternatives using the results from M87$^{*}$ observation. We find that, for
the mass, inclination angle and the angular diameter of the shadow of M87$^{*}$
reported by the EHT collaboration, the maximum value of the parameter $r_0$
must be in the range $2.54r_{+}\leq r_{0,max}\leq 3.51r_{+}$ for the
dimensionless spin range $0.5\leq a_{*}\leq 0.94$, with $r_{+}$ being the outer
horizon radius of the Kerr black hole at the corresponding spin value. We
conclude that these black hole alternatives having $r_0$ below this maximum
range (i.e. $r_0\leq r_{0,max}$) is consistent with the size and deviation from
circularity of the observed shadow of M87$^{*}$.
