We study the possible tetraquark interpretation of light scalar meson states a₀(980), f₀(980), κ, σ within the framework of the non-relativistic potential model. The wave functions of tetraquark states are obtained in a space spanned by multiple Gaussian functions. We find that the mass spectra of the light scalar mesons can be well accommodated in the tetraquark picture if we introduce a three-body quark interaction in the quark model. Using the obtained multiple Gaussian wave functions, the decay constants of tetraquarks are also calculated within the ``fall apart'' mechanism.