  We examine the possibility for the existence of gravitomagnetic monopole
($n_*$) in M87* by using the results obtained from its first Event Horizon
Telescope image. By numerically deducing the shadow sizes in Kerr-Taub-NUT
(KTN) spacetime, we show that the shadow size increases with increasing $|n_*|$
for a fixed Kerr parameter $|a_*|$ in case of the KTN black hole, whereas for a
KTN naked singularity it increases with increasing $n_*$ for a fixed $a_* > 0$
if $n_* > -\cot 17^{\circ}$ . In general, the asymmetry of shadow shape
increases if the central dark object in M87 is a KTN/Kerr naked singularity
instead of a KTN/Kerr black hole. We find that a non-zero gravitomagnetic
monopole is still compatible with the current EHT observations, in which case
the upper limit of $n_*$ cannot be greater than $1.1$, i.e., $n_* \lesssim 1.1$
for the prograde rotation ($a_* > 0$), and the lower limit of $n_*$ cannot be
less than $-1.1$, i.e., $ n_* \gtrsim -1.1$ for the retrograde rotation ($a_* <
0$). Moreover, if the circularity of the shadow can be measured on a precision
of $\lesssim 1\%$, the Kerr and KTN naked singularities can be falsified for
M87*.
