  We formulate an extended linear $\sigma$ model of a quarkonia nonet and a
tetraquark nonet as well as a complex iso-singlet (glueball) by virtue of
chiral symmetry $SU_L(3) \times SU_R(3)$ and $U_A(1)$ symmetry. In the linear
realization formalism, we study the mass spectra and components of the
low-lying scalars and pseudo scalars in this model. The mass matrices for
physical staes are obtained and the glueball candidates are examined. We find
that the model can accommodate the mass spectra of low-lying states quite well.
Our fits indicate that the most glueball like scalar should be 2 GeV or higher
while the glueball pseudoscalar is $\eta(1756)$. We also examine the parameter
region where the lightest iso-scalar $f_0(600)$ can be the glueball and
quarkonia dominant but find such a parameter region may be confronted with the
problem of the unbounded vacuum from below.
