We analyse two-dimensional near-IR K - band spectra from the inner 660 \times 315 pc ^ { 2 } of the Seyfert galaxy NGC 7582 obtained with the Gemini GNIRS IFU at a spatial resolution of \approx 50 pc and spectral resolving power R \approx 5900 . The nucleus harbors an unresolved source well reproduced by a blackbody of temperature T \approx 1050 K , which we attribute to emission by circumnuclear dust located closer than 25 pc from the nucleus , with total mass of \approx 3 \times 10 ^ { -3 } M _ { \odot } . Surrounding the nucleus , we observe a ring of active star formation , apparently in the galactic plane , with radius of \approx 190 pc , an age of \approx 5 Myr and total mass of ionized gas of \approx 3 \times 10 ^ { 6 } M _ { \odot } . The radiation of the young stars in the ring accounts for at least 80 % of the ionization observed in the Br \gamma emitting gas , the remaining being due to radiation emitted by the active nucleus . The stellar kinematics was derived using the CO absorption band at 2.29 \mu m and reveals : ( 1 ) a distorted rotation pattern in the radial velocity field with kinematic center apparently displaced from the nuclear source by a few tens of parsecs ; ( 2 ) a high velocity dispersion in the bulge of \sigma _ { * } = 170 km s ^ { -1 } ; ( 3 ) a partial ring of \sigma _ { * } = 50 km s ^ { -1 } , located close to the Br \gamma emitting ring , but displaced by \approx 50 pc towards the nucleus , interpreted as due to stars formed from cold gas in a previous burst of star formation . The kinematics of the ionized gas shows a similar rotation pattern to that of the stars , plus a blueshifted component with velocities \geq 100 km s ^ { -1 } interpreted as due to an outflow along the ionization cone , which was partially covered by our observations . The mass outflow rate in the ionized gas was estimated as \dot { M } _ { HII } \approx 0.05 { M _ { \odot } yr ^ { -1 } } , which is one order of magnitude larger than the accretion rate to the active galactic nucleus ( AGN ) , indicating that the outflowing gas does not originate in the AGN , but is instead the circumnuclear gas from the host galaxy being pushed away by a nuclear outflow . The flux distribution and kinematics of the hot molecular gas , traced by the H _ { 2 } \lambda 2.22 \mu m emission line , suggests that most of this gas is in the galactic plane . An excess blueshift along PA \approx - 70 ^ { \circ } , where a nuclear bar has been observed , can be interpreted as an inflow towards the nucleus . We thus conclude that the H _ { 2 } kinematics traces the feeding of the AGN , while the ionized gas kinematics traces its feedback via the outflows . An AGN-Starburst connection in the nucleus of NGC 7582 is supported by the ratio between the mass accretion rate and the star formation rate in the circumnuclear region of \approx 0.26 % , which is close to the expected relation between the mass of the SMBH and that of the host galaxy bulge in galaxies ( the Magorrian relation ) .