The 68-year-old insists his priority is to strengthen the club as Indonesian businessman Erick Thohir nears a takeover deal
The Indonesian businessman looks set to become majority shareholder at the Serie A club after months of speculation, during which Moratti's future at San Siro has been shrouded in doubt.
However, the 68-year-old has been left delighted with the amicable talks with Thohir to date, and claims he could yet stay in his post as he looks for the best possible arrangement for the club.
"There's still time to think about [remaining president]," he told Sky Sport 24.
"But that just shows you the friendly approach Thohir has taken and it also shows you that we're two groups who both want to strengthen the club – that's the main thing.
"It's not about one group taking over from another. There are two groups which, as I said, want to strengthen the club. Two families. That appeals to Thohir and it appeals to me too."
Inter have made a promising start to the Serie A season, taking 10 points from a possible 12, following their dismal ninth-placed finish last season.
Moratti is pleased with their campaign so far and dismissed suggestions that the forthcoming games against Fiorentina and Roma would shape their season.
"It's far too early for that; these are still the first few games," he said.
"We're pleased with the strong start we've made. There's a great mood in the camp and the coach has proven his quality.
"There are players who have shown their talent and others who have shown glimpses of it. That's all very pleasing but naturally we want to keep on improving with every game.
"Certain players are showing how much individual talent they have, that's clear to see. They're doing their jobs very well, assuming their responsibilities and sticking to the coach's game plan. They're doing great."