The five Taliban leaders traded a year ago for Sgt. Bowe Bergdahl could be free to travel as early as Monday as the terms of their supervised release are set to expire, raising alarm on Capitol Hill about the possibility they could return to the battlefield.

The five former Guantanamo detainees have been under close monitoring in Qatar and subject to a travel ban since their release last year. The agreement with Qatar is set to expire June 1.

While the Washington Post reported earlier this month that the administration was in talks with Qatari officials about potentially extending security measures for the group, it's unclear if any restrictions will remain in place after the end of the month.

Asked this week if the talks produced any agreement, a State Department official told FoxNews.com, "We don't have any updates."

Congressional lawmakers have grown anxious.

Joe Kasper, spokesman for House Armed Services Committee member Rep. Duncan Hunter R-Calif., said his office has gotten "radio silence" from the administration in asking about the issue.

"They have to be concerned with what happens to the five Taliban because they made every effort to portray the trade as a good deal," Kasper said in an email. "The nightmare scenario for the Administration is if any of these guys show up again within the global battlespace, be it in some kind of leadership position or just as messengers of threats or propaganda."

Members of Congress have repeatedly expressed concern about what will happen after the travel ban expires. They have asked the Obama administration to try to persuade Qatar to extend the monitoring.

"It's impossible for me to see how they don't rejoin the fight in short order," said Rep. Ed Royce, R-Calif., chairman of the House Foreign Affairs Committee.

Sen. Kelly Ayotte, R-N.H., wrote Defense Secretary Ash Carter in March, asking him to take any step necessary to make sure the five do not return to the battlefield in Afghanistan.

On Wednesday, she reiterated that appeal. "With restrictions on the Taliban Five reportedly expiring, I urge the administration to take every necessary measure to ensure they are not permitted to return to the battlefield in Afghanistan. Our troops should never have to confront a former Gitmo detainee on the battlefield," she said in a statement to FoxNews.com.

Rep. Adam Schiff of California, the top Democrat on the House Intelligence committee, noted Congress spent a lot of time debating whether the five would be adequately monitored during the first 12 months. "My point all along was that I'm more worried about month No. 13 than the first 12," he told The Associated Press.

Schiff has been privy to the details of the still-secret memorandum of understanding the U.S. reached with Qatar that put the five under a 12-month watch following their release. "The Qataris did pretty good -- I wouldn't say perfect," he said about the year-long monitoring. "But the big question is what comes next."

Fox News reported in March that, according to a government official familiar with the intelligence, at least three of the five have tried to plug back into their old terror networks.

The Post reported earlier this month that amid these concerns, administration officials were putting several options on the table for keeping some restrictions in place. At the time, State Department spokesman Jeff Rathke confirmed the administration was in talks to limit or "mitigate" the risk of former Guantanamo prisoners returning to terrorism. While not mentioning the Taliban Five by name, Rathke did not deny the Post report that these talks were designed to extend the restrictions that expire at the end of the month.

But there was no public indication Tuesday, with just days left on the Qatari deal, on whether the talks led anywhere. Rathke also said Tuesday he had no updates on the issue.

The administration, meanwhile, continues to take heat for last year's trade.

After a lengthy investigation, Bergadhl is being brought up on desertion charges. And on Tuesday, former commander of U.S. forces in Afghanistan Gen. Stanley McChrystal told Fox News that his "initial understanding" of Bergdahl's disappearance was that he had walked off the base intentionally.

Fox News had reported in April that, according to Bergdahl's platoon mates, then-Chairman of the Joint Chiefs of Staff Adm. Mike Mullen also knew those details. With McChrystal's comments, this would indicate two of the most-senior military commanders understood the alleged circumstances of Bergdahl's departure, raising more questions about the Taliban-Bergdahl trade itself and the way the deal was initially portrayed to the public.

White House Press Secretary Josh Earnest, asked Tuesday about McChrystal's comments and whether President Obama also was told Bergdahl walked off the base, did not respond directly.

He cited the ongoing military "process" underway, and said: "I'm not going to weigh in on this particular situation until that justice process has run its course."

He reiterated that Obama, as commander-in-chief, has a "special responsibility" to live up to the "principle" that no one in a U.S. military uniform is left behind.

FoxNews.com's Judson Berger, Fox News' Catherine Herridge and The Associated Press contributed to this report.