  Black holes carrying a magnetic monopole charge are a subject of interest for
a long time. In this work we explore the possibility of an observational
evidence of such black holes carrying a magnetic monopole, namely the Bardeen
rotating black holes. We derive the theoretical spectrum from the accretion
disk surrounding a Bardeen black hole using the thin-disk approximation. We
compare the theoretically derived spectrum in comparison to the optical data of
eighty Palomar Green quasars to constrain the monopole charge parameter $g$ and
the spin parameter $a$ of the quasars. From our analysis we note that the
Kerr-scenario in \gr\ is observationally more favored than black holes with a
monopole charge. We arrive at such a conclusion using error estimators like
$\chi^2$, the Nash-Sutcliffe efficiency, the index of agreement and their
modified forms. In particular, black holes with $g \geq 0.03$ are outside
$99\%$ confidence interval. The implications are discussed.
