We calculate the mass of tetraquark states of all $qqbar q bar q$ quark configurations in a constituent quark model where the Cornell-like potential and one-gluon exchange spin-spin coupling are employed. The three coupling parameters for the Cornell-like potential and one-gluon exchange spin-spin coupling are proposed mass-dependent in accordance with Lattice QCD data, and all model parameters are predetermined by studying light, charmed and bottom mesons. The theoretical predictions for light tetraquarks are compared with the observed exotic meson states in the light-unflavored meson sector, and tentative assignments are suggested. The work suggests that the $f_0(1500)$ and $f_0(1710)$ might be ground light tetraquark states with $J=0$.
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