Fidel Castro's death has opened doors for U.S.-Cuba relations to grow warmer and President-elect Donald Trump should be open to talks with our neighbor to the south, former Commerce Secretary Carlos Gutierrez said Monday.

The Cuba-born Gutierrez, who was commerce secretary under President George W. Bush and currently chairs the Albright Stonebridge Group, said that with U.S. companies getting closer to Cuba over the last several years, the only way to move, at least in terms of economic interests, is forward.

"A lot of work has been done, and I think that the president-elect would be well-served if he received other points of view," Gutierrez told CNBC's "Squawk Box."

Gutierrez was interviewed before Trump warned in a tweet on Monday that he would break off the fledgling ties unless Cuba negotiated a better agreement with the United States.

On Saturday, after the death of Fidel Castro, Trump released a statement that called the former leader a "brutal dictator who oppressed his own people for nearly six decades."

Gutierrez said it would be wise for Trump to consider the benefits of having economic dealings with Cuba, citing businesses, universities, hospitals and other organizations that have worked hard over the last two years to establish ties with Cuba.

"He's getting a lot of pressure to just write everything off, and there are a lot of businesses, a lot of farm states, a lot of governors, a lot of mayors who are counting on agricultural sales to Cuba," Gutierrez said.

The former secretary added that a number of airlines have spent a considerable amount of time and money setting up regular flight patterns to Cuba, and that Starwood Hotels is already managing hotels there. JetBlue resumed commercial flights on Monday.

Gutierrez said Trump should take the opportunity to get everything on the table and discuss the country's options rather than rolling back President Barack Obama's progress with normalization.

"I think it would be a tremendous legacy for … President-elect Trump to be the businessperson who can spread the word of how noble free enterprise is. This is a perfect opportunity to do it in Cuba, and I do believe that he is just hearing one side of the story," Gutierrez said.

Yet some, like Rep. Carlos Curbelo, R-Fla., argue that not much negotiation has occurred even under Obama.

Curbelo called Obama's push for normalizing ties with Cuba a "legacy-building exercise" and said that so far, talks with Cuba have resembled a one-sided giveaway.

"The end [goal] is for Cuba to be a free and democratic nation and a true partner for the United States, a country where U.S. companies and Americans can actually feel comfortable visiting and doing business," Curbelo told "Squawk Box."

"What we're going to see, or at least we hope, after President-elect Trump takes over on January 20 is a policy that actually holds the Cuban government accountable not just to make economic reforms, but also to make political reforms," he said.

Curbelo, a son of Cuban exiles, said some simple demands could include asking Cuba to scale down its spy network, by which the Cuban government allegedly sells U.S. information to countries like Russia and North Korea. He also said Cuba should stop harboring U.S. fugitives, stop interfering in the United States' bilateral trade with Venezuela and stop oppressing its people.

"Everyone wants to help the Cuban people, what we don't want to do is help the Cuban dictatorship and strengthen that dictatorship," Curbelo said.

American University government professor William LeoGrande said the Cuban people are generally positive on Cuba improving its ties with the United States.

"There are a lot of stakeholders involved in the policy that Barack Obama put in place, not least among them ordinary Cubans, who are overwhelmingly in favor of better relations with the United States because it means more tourism and more trade, and that boosts the Cuban economy and ultimately boosts their standard of living," LeoGrande told "Squawk Box."

Echoing Gutierrez, LeoGrande mentioned that U.S. companies have already established themselves in Cuba in anticipation of warmer relations.

"Starwood Hotels, Airbnb — those are constituencies that think that the U.S. policy that Obama put in place is actually working," he said.

With many Cubans worried that Trump will reverse Obama's efforts and "throw us back to Cold War era of hostility," LeoGrande said that simply, "there needs to be more mutual respect."