In the interview, Cook cast the trade-related economic weakness in China as "temporary," saying it was in both countries' "best interests" to reach an agreement.
"It is a very complex trade agreement and it needs to be updated, but as I've said before, I'm very optimistic that this will happen," Cook told Cramer. "That clearly will be good not only for us, frankly, but I think more about the world in general. The world needs a strong U.S. and China economy for the world economy to be strong."
The U.S. and China will continue trade talks in Beijing for an unscheduled third day, a member of the U.S. delegation said on Tuesday, as the world's two largest economies looked to resolve their bitter trade dispute.
In the interview with Cramer, Cook said he had "heard some very encouraging words" from people with knowledge of the talks "very recently," and had shared his thoughts and concerns with them.
"I felt that Tim came very close to saying that we could have a real breakthrough with China," Cramer said on television after the interview. "He was so encouraging, and he said his information was recent."