EXCLUSIVE: At least three of the five Taliban leaders traded last year for Sgt. Bowe Bergdahl have tried to plug back into their old terror networks, a government official familiar with the intelligence told Fox News, describing it as an attempt to "re-engage."

The new allegations come as Bergdahl now faces desertion charges, and as the one-year deal governing the former Guantanamo detainees' supervised release in the Gulf nation of Qatar is set to expire -- at the end of May.

The director of the Defense Intelligence Agency recently told Congress that, after that expiration, all his officers can do is warn the U.S. government if the men return to the battlefield.

"I've seen nothing that causes me to believe these folks are reformed or [have] changed their ways or intend to re-integrate to society in ways to give me any confidence that they will not return in trying to do harm to America," Rep. Mike Pompeo, R-Kan., a member of the House intelligence committee, told Fox News.

The official who described the attempts by three to make contact did not identify the men by name. But the evidence came to light through intelligence from liaison services and monitored communications available to the U.S. government.

A defense official did not dispute the claim, emphasizing that one of the men has come "very close, trying to provide advice, council or inspiration" to his terror network, while the other two had not crossed that line.

In January, CNN was first to report, and U.S. officials later confirmed, that one of the five fighters was making phone calls to militants. The latest claim indicates those efforts were more widespread.

A State Department official, though, disagreed with the characterization of the intelligence and how it relates to the "Taliban Five's" activities.

"None of the five individuals has returned to the battlefield and none of the five have left Qatar," the official said. "Since their transfer many actions have been taken to restrict the actions of these individuals, and they are all being closely monitored by the United States and Qatar.

"We are in frequent and high level contact with Qatari government about the implementation of these measures, to ensure our concerns about these individuals are being met. For example, by enabling us to closely track their activities."

The Office of the Director of National Intelligence also uses a strict definition for re-engagement, saying they do not "consider mere communication with individuals or organizations -- including other former GTMO detainees -- an indicator of reengagement. Rather, the motives, intentions, and purposes of each communication are taken into account when assessing whether the individual has reengaged."

Separately, a military intelligence source told Fox News that "multiple options" were on the table in the Bergdahl case that did not involve the swap of the Taliban Five -- but the administration's preferred option was to secure the Army sergeant's freedom through the controversial transfer.

Fox News is told that the options included a so-called snatch-and-grab rescue mission, using and paying a contractor to find and rescue him, as well as working through the Pakistani intelligence service also known as the ISI.  The account was backed up by a separate government source. The House Armed Services Committee, which is investigating the swap, declined to comment.

The military intelligence source also characterized the data provided by Bergdahl's debriefings -- which included intelligence about his route from Afghanistan into Pakistan as well as information about his captors -- as "dated, historical" and "worthless." The substance of the Bergdahl briefings was not disputed by the defense official.

Neither the CIA, Pentagon nor National Security Council press offices offered on-the-record comment about the Bergdahl case. Fox News is told Qatar has cracked down on the men's communications since it was first reported that one of them was trying to reach out. A defense official said any effort by the men to reconnect is "of interest to the U.S.," and provides greater visibility into the remaining terror networks.

In a March report on Guantanamo detainees who have returned to the fight, the Taliban Five detainee first suspected of attempting to re-engage was not listed in the "suspected" category. Only one of the intelligence agencies reportedly disagreed with that assessment.