The Inter chief also revealed there is a "small chance" the playmaker could remain at San Siro, with the player himself adding that both eventualities are still possible
The Netherlands international has been dragging his heels over a possible move to Turkey ever since the two sides agreed a transfer fee at the beginning of the month, but Moratti has revealed that progress has been made after he met with the player in person.
"We needed this meeting and it was pleasant," he told Sky Italia. "There is still a small chance that Sneijder could stay. Is he closer to Galatasaray now? I think so, yes."
Sneijder then echoed the words of the Nerazzurri supremo, adding: "I have loved and do love this team. The Inter fans are the most important thing for me.
"I cannot talk about the negotiations right now, but I agree with the president's words."
Goal.com exclusively revealed earlier this week that Liverpool had stepped up their interest in the 28-year-old following his impasse with Galatasaray, with the player thought to be keen on a move to England.
Reds captain Steven Gerrard admitted on Sunday that he "would love nothing better" than to see the midfielder join the Anfield outift, but suggested his wage demands might potentially prove problematic.