There is increasing evidence for the presence of blue super star clusters in the central regions of ultraluminous infrared galaxies like Arp 220. Ultraluminous galaxies are thought to be triggered by galaxy mergers, and it has often been argued that these super star clusters may form during violent collisions between gas clouds in the final phase of the mergers. We now investigate another set of models which differ from previous ones in that the formation of the super star clusters is linked directly to the very intense starburst occurring at the very center of the galaxy. Firstly we show that a scenario in which the super star clusters form in material compressed by shock waves originating from the central starburst is implausible because the objects so produced are much smaller than the observed star clusters in Arp 220. We then investigate a scenario (based on the Shlosman-Noguchi model) in which the infalling dense gas disk is unstable gravitationally and collapses to form massive gaseous clumps. Since these clumps are exposed to the external high pressure driven by the superwind (a blast wave driven by a collective effect of a large number of supernovae in the very core of the galaxy), they can collapse and then massive star formation may be induced in them. The objects produced in this kind of collapse have properties consistent with those of the observed super star clusters in the center of Arp 220.