  The Event Horizon Telescope (EHT) observation unveiled the first image of
supermassive black hole Sgr A* showing a shadow of diameter $\theta_{sh}= 48.7
\pm 7\,\mu$as with fractional deviation from the Schwarzschild black hole
shadow diameter $\delta =
-0.08^{+0.09}_{-0.09}~\text{(VLTI)},-0.04^{+0.09}_{-0.10}~\text{(Keck)}$. The
Sgr A* shadow size is within $~10\%$ of the Kerr predictions, providing us with
another tool to investigate the nature of strong-field gravity. We use the Sgr
A* shadow observables to constrain metrics of four independent and
well-motivated, parametrically different from Kerr spacetime, rotating regular
spacetimes, and the corresponding no-horizon spacetimes. We present constraints
on the deviation parameter $g$ of rotating regular black holes. The shadow
angular diameter $\theta_{sh}$ within $1 \sigma$ region, places bounds on the
parameters $a$ and $g$. Together with EHT bounds on $\theta_{sh}$ and $\delta$
of Sgr A*, our analysis concludes that the three rotating regular black holes,
viz., Bardeen Hayward, and Simpson-Visser black holes, and corresponding
no-horizon spacetimes agree with the EHT results of Sgr A*. Thus, these three
rotating regular spacetimes and Kerr black holes are indiscernible in some
parameter space, and one can not rule out the possibility of the former being
strong candidates for astrophysical black holes.
