We present the first interferometric HCN ( J = 3–2 ) and HCO ^ { + } ( J = 3–2 ) maps in the circumnuclear region of NGC 1097 , obtained with the Submillimeter Array . The goal is to study the characteristics of the dense gas associated with the starburst ring/Seyfert nucleus . With these transitions , we suppress the diffuse low density emission in the nuclear region . We detect and resolve the individual compact giant molecular cloud associations ( GMAs ) in the 1.4 kpc circumnuclear starburst ring and within the 350 pc nuclear region . The nucleus is brighter than the ring in both lines , and contributes to \sim 20 \% and \sim 30 \% to the total detected HCO ^ { + } ( J = 3–2 ) and HCN ( J = 3–2 ) flux , within the central 1.4 kpc . The intensity ratios of HCN ( J = 3–2 ) /HCO ^ { + } ( J = 3–2 ) are roughly unity in the GMAs of the starburst ring . However , this ratio is up to \sim 2 in the nuclear region . From the HCN ( J = 3–2 ) /HCN ( J = 1–0 ) ratio of \leq 0.2 in the nucleus , we infer that the nuclear HCN ( J = 3–2 ) emission might be optically thin . The HCO ^ { + } ( J = 3–2 ) and HCN ( J = 3–2 ) show correlations with ^ { 12 } CO ( J = 3–2 ) and the 24 \micron  emission . The tight correlations of HCN ( J = 3–2 ) , HCO ^ { + } ( J = 3–2 ) and 24 \micron emission in the starburst ring suggest that the dense molecular gas and the dust are from the same origins of star forming regions . On the other hand , the HCN ( J = 3–2 ) emission of the nucleus is significantly enhanced , indicating mechanisms other than star formation , such as AGN activities . A self-consistent check of the fractional abundance enhanced by X-ray ionization chemistry of the nucleus is possible with our observations .