We present a pilot study of \sim 3 ^ { \prime \prime } resolution observations of low CO transitions with the Submillimeter Array in three nearby Seyfert galaxies , which are part of the low-luminosity quasi-stellar object ( LLQSOs ) sample consisting of 99 nearby ( z = 0.06 ) type-1 active galactic nuclei ( AGN ) taken from the Hamburg/ESO quasi-stellar object ( QSO ) survey . Two sources were observed in ^ { 12 } CO ( 2–1 ) and ^ { 13 } CO ( 2–1 ) and the third in ^ { 12 } CO ( 3–2 ) and HCO ^ { + } ( 4–3 ) . None of the sources is detected in continuum emission . More than 80 % of the ^ { 12 } CO detected molecular gas is concentrated within a diameter ( FWHM ) < 1.8 kpc . ^ { 13 } CO is tentatively detected , while HCO ^ { + } emission could not be detected . All three objects show indications of a kinematically decoupled central unresolved molecular gas component . The molecular gas masses of the three galaxies are in the range M _ { \textrm { mol } } = ( 0.7 - 8.7 ) \times 10 ^ { 9 } M _ { \odot } . We give lower limits for the dynamical masses of M _ { \textrm { dyn } } > 1.5 \times 10 ^ { 9 } M _ { \odot } and for the dust masses of M _ { \textrm { dust } } > 1.6 \times 10 ^ { 6 } M _ { \sun } . The R _ { 21 } = ^ { 12 } CO/ ^ { 13 } CO ( 2–1 ) line luminosity ratios show Galactic values of R _ { 21 } \sim 5 - 7 in the outskirts and R _ { 21 } \gtrsim 20 in the central region , similar to starbursts and ( ultra ) luminous infrared galaxies ( ( U ) LIRGs ; i.e . LIRGs and ULIRGs ) , implying higher temperatures and stronger turbulence . All three sources show indications of ^ { 12 } CO ( 2–1 ) / ^ { 12 } CO ( 1–0 ) ratios of \sim 0.5 , suggesting a cold or diffuse gas phase . Strikingly , the ^ { 12 } CO ( 3–2 ) / ( 1–0 ) ratio of \sim 1 also indicates a higher excited phase . Since these galaxies have high infrared luminosities of L _ { \textrm { IR } } \geq 10 ^ { 11 } L _ { \odot } and seem to contain a circumnuclear starburst with minimum surface densities of gas and star formation rate ( SFR ) around \Sigma _ { mol } = 50 - 550 M _ { \odot } ~ { } pc ^ { -2 } and \Sigma _ { \textrm { SFR } } = 1.1 - 3.1 M _ { \odot } ~ { } kpc ^ { -2 } yr ^ { -1 } , we conclude that the interstellar medium in the centers of these LIRG Seyferts is strongly affected by violent star formation and better described by the ULIRG mass conversion factor .