Santa Cruz regained his WBA featherweight title on a majority verdict in Las Vegas on 28 January.
Frampton won the first contest between the pair six months earlier and wants the trilogy to be completed in Belfast.
"I'm hoping that Leo sticks to his word and comes to Belfast like he said. He can make it happen," said Frampton.
Santa Cruz hinted after the fight that he had other options in addition to a possible rematch with the Northern Irishman, and that his promoters would also have a major say in the next step of his career.
"Negotiations are at a very early stage but our team are slightly more optimistic than we were initially after the fight," said Frampton.
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"He's the man that's fighting so he can make the decision and pull the strings. If he wants to come to Belfast he tells the promoter what he wants to do."
Frampton, 29, who suffered the first defeat of his career at the MGM Grand Garden Arena, also reiterated his desire for his next fight to be staged at Windsor Park, home stadium of the Northern Ireland football team.
"I want to fight in Belfast next. I want to fight at home. I feel like I've been on the road now for about two years or so," he said.
"If it's not him, I'll be fighting in Belfast against someone else, although I don't know who that is.
"That's what I've wanted to do for a long time. It's been a dream of mine to fight at Windsor Park. I was in the stadium tonight and it looks outstanding.
"I can just imagine a ring right in the middle of it and winning back my title at Windsor would be a dream come true."
Carl Frampton says his team are "slightly more optimistic in the last few days" about the prospect of a third fight with Mexican Leo Santa Cruz.