Petroleum tycoon Moratti, who was president and owner when Inter won a league, Cup and Champions League treble in 2010, has held an honorary president's role after selling a 70 percent stake to Indonesian Erick Thohir in November 2013.
But Moratti gave the biggest indication yet he could be about to cut his family's decades-old ties with the club and sell his 29.5 percent share after a shareholders' meeting on Monday. The remaining 0.5 percent share is held by other, minority shareholders.
"When you're useful, or even better, necessary, you stay. But when you realise that outside of the affection and niceness there's nothing, it's best to do something else," Moratti told reporters.
Moratti on Sunday confirmed reports from last week that his stake was up for sale. Following Inter's scoreless draw at home to champions Juventus, he said: "My stake is always available to the shareholders."
But there are conflicting reports as to who could step in. Thohir and Etihad Airways have already been touted as possible purchasers of Moratti's stake, although the club remain coy on the reported involvement of the Emirati company.
Reports on Sunday claimed Etihad would replace Pirelli as the Serie A giants' new shirt sponsor, with a five-year deal worth €125 million ($125 million) in the pipeline.
If it goes through, it would be a huge boost to Roberto Mancini's side. Inter currently earn €12 million a season with tyre giants Pirelli, who have been linked to the club for close to 20 years, but the current deal expires at the end of the season.
Yet on Monday, Inter's corporate director Michael Williamson suggested negotiations with Pirelli about a new deal are ongoing.
"As for new sponsors, negotiations with Pirelli are still going ahead, they are our historic partner and we want to continue working together," said Williamson.
"Negotiating with other parties is a part of this process for the interests of shareholders. Nevertheless, we are at an advanced stage in talks with Pirelli."
Thohir has insisted he is keen to retain the current set-up.
"Basically we do not intend to change the set-up we have at the moment. Things have gone well so far, we're pleased and we're very respectful of this relationship," he said.
But he has instigated significant changes at Inter since taking over, luring Mancini back to the club as well as buying a number of the players the coach had on his shopping list.
The Indonesian tycoon has also brought several new faces on to the board, a development that is believed to have pushed Moratti out on to the fringes at club meetings and consultations.
Asked how he felt about not being so involved, Moratti said: "It suits me fine, and they are all very happy, but time is passing."
On paper, Inter have one of the strongest squads in the league this year and it has shown: Mancini's men won their opening five games and currently sit third, just one point behind leaders Fiorentina.