The 68-year-old stepped down from the position after selling his 70 per cent stake in the club to Indonesian businessman Erick Thohir in October.
Moratti is now listed as Inter's honorary president, with son Angelomario Moratti serving as vice-president.
Oil tycoon Moratti worked as Inter president for 18 years, but has no desire to do so again.
"To return now as president would be crazy, but perhaps one day my son might do it, I do not rule that out," he told Milan-based TV station Telelombardia.
"Taking on Inter to me was like running away with a blonde. Now I am glad to be in the club as a partner. It's a matter of the heart and I have to thank Thohir."
Inter won five Serie A titles, the UEFA Champions League, the UEFA Cup and the FIFA Club World Cup during Moratti's time at the helm.
However, the club have struggled to replicate those glories in recent years, and sit fifth in Serie A ahead of Sunday's visit of Atalanta.
