James Rosen, Fox News' chief Washington correspondent, reported Thursday during "Special Report" about the speculation on whether Secretary of State John Kerry was left out of the loop on President Obama's historic policy shift on Cuba.

Since the December announcement by Obama, Rosen said foreign policy circles have been buzzing about how much the State Department really knew about the initiative.

Fox News reported:

“The reality is that the way this whole thing was negotiated was not exactly out of a textbook,” said David Rothkopf, CEO and editor of the influential magazine and website Foreign Policy, and a supporter of the president’s policy shift. “And while the White House gets credit for keeping some of it secret, the way I understand it is a lot of it was secret from the State Department until just over a week before the deal.”

Sen. Marco Rubio, R-Fla., a Cuban-American lawmaker who sits on the Foreign Relations Committee and has been fiercely critical of the policy shift – arguing that the U.S. failed to extract significant concessions from the Castro regime on its abysmal human rights record – told Fox News the furtive means employed in the Cuba talks helped to produce what he sees as an unsatisfactory outcome.

The White House has said that two of its National Security Council staffers led the secret talks, not Kerry or his point person on Cuba.

Aides to Kerry, though, deny he was out of the loop, adding he was comfortable with the process.

Rosen added that Cuban-American Sen. Robert Menendez (D-N.J.) is concerned about the deal Obama brokered for the policy shift. 

"It's going to create a doubt in my mind when State Department witnesses come before the committee," Menendez told Rosen. "Are they either telling us the entire truth, or are they just shunned out of the process by the White House? Either way, it's going to create some real concerns (over) the veracity of what we're hearing in testimony, as we move forward.”

Watch the video above to hear more from Rosen.