The Serie A giants undertook the latest stage of their rebuilding process with the financial backing of the Suning Holdings Group, which acquired a majority stake in Inter last June, during the current transfer window.
Premier League champions Chelsea and Inter were both linked with a move for the 30-year-old but Rummenigge insists such talk was wide of the mark in terms of formal offers.
"Nobody asked us for him and there was never an official offer for him, not even this summer when the market was open," he told Mediaset.
"So I cannot confirm Inter wanted him."
Luciano Spalletti, head coach of the Italians, added Milan Skriniar, Borja Valero, Matias Vecino, Dalbert, Joao Cancelo and Yann Karamoh to his squad for 2017-18 and also retained Ivan Perisic amid reports of sustained interest from Manchester United.
They began the season with a 3-0 win over Fiorentina but Spalletti's former club Roma dealt out a 3-1 defeat ahead of the international break, during which Vidal's Chile had their World Cup hopes placed in jeopardy by back-to-back defeats against Paraguay and Bolivia.