The senators had expressed concern terrorism detainees from the Guantanamo Bay Detention Camp would be relocated to the U.S. Disciplinary Barracks military prison at the Fort Leavenworth U.S. Army post in Kansas.
"We believe that the administration has a good understanding of obstacles and concerns and is giving them proper consideration," Brownback and Roberts said in a joint statement.
"We are confident that because of this good-faith dialogue, detainees will not be transferred to Fort Leavenworth."
Neither would offer details about their talks with the administration or whether any promises had been made concerning Fort Leavenworth, The Kansas City (Mo.) Star reported.
The White House had no comment.
The possibility of moving detainees to Kansas from Cuba emerged last winter when U.S. President Barack Obama pledged to close the detention camp by January 2010.
Kansas lawmakers and officials said the prison, popularly known as the DB or the Castle, was not suitable and worried the detainees' presence could put the surrounding community at risk, the Star said.
Leavenworth is the U.S. military's only maximum-security facility.
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