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."
According to Cramer, host of "Mad Money," Cook said "'my information is basically real time,' and real-time, he feels a lot better … about a possible China deal." Cook was "more bullish than I was," Cramer adds.
Last week, Apple lowered its first-quarter guidance, citing economic weakness in China as one of the reasons for the pain. Cook later told CNBC he believed U.S.-China "trade tensions" exacerbated the slowdown in China.
If the two countries are able to reach a deal, that will mean good things for Apple's stock, which closed nearly 2 percent higher on Tuesday, Cramer argued.
"It would be a big breakthrough and make people feel like they should be buying shares of Apple at their current levels," he said. "I took [Cook's remarks] as real upside and it made me feel like the stock is in the process of bottoming here."
Cook also told Cramer that Apple's growing ecosystem of devices and services is "probably underappreciated" by the naysayers on Wall Street.
— Reuters contributed to this story.
Disclosure: Cramer's charitable trust owns shares of Apple.