The Argentine, who will turn 41 in August, has long been expected to retire this summer but had repeatedly stated that he had no interest in taking up a coaching role with the Nerazzurri.
However, according to Thohir, the iconic defender was only too happy to accept an administrative position at San Siro.
"I met with Zanetti some months ago in order to understand his vision," the Indonesian businessman told reporters on Tuesday.
"He will be part of the directors, but we're agreed that for now he needs to contrate on the final games he has to play."
Thohir also spoke about his desire to strengthen Walter Mazzarri's playing squad during the summer but he refused to be drawn on whether signing Manchester City striker Edin Dzeko was likely to become reality or remain a dream.
"It can be anything," he countered. "But I only announce the players that we sign, not the players that we dream about."