The 28-year-old Dutch international has been holding talks with the Turkish giants since Moratti accepted a 10million euro bid for his services two weeks ago.
Sneijder was reported to be upset when Moratti urged a "professional" decision over his future, one that would bring an unpleasant contract dispute to a close while ending the player's three-and-a-half-year association with the Serie A club.
Moratti has not closed the door on Sneijder, who won the treble in 2010, but revealed the Dutchman could join Galatasaray in the next few days.
He told inter.it: "I met Sneijder. I wanted to have a chat with him, I thought we needed to.
"Have we made peace? I don't think there was ever a war in the first place, and certainly not with me personally.
"Did we chat to see if we were all moving in the same direction? Which one? It's a surprise...
"Is he close to a move to Galatasaray? Yes, I think so."
Sneijder has not featured for Inter since September after publicly rejecting a request to take a two million euro pay cut on his annual salary, but head coach Andrea Stramaccioni insists his absence from the first team has been solely a tactical decision.
Following his conversation with Moratti, the playmaker appeared ready to concede his successful career at the San Siro is coming to end.
"I spoke a lot with president Moratti because we have a good relationship, we had a good talk, nothing more than that," he told inter.it.
"He said that it's looking like I'll be off to Galatasaray but there's still a slim chance I could stay? What the president said is exactly right.
"The Inter fans expect me to stay? Inter fans are the best around, I've won everything here and I'm happy here.
"Now I don't know whether I'll be saying, 'I am happy here' or 'I was happy here'. One of two things could happen, we'll see."