Federal officials are expected to visit the maximum security Thomson Correctional Center, about 150 miles west of Chicago, on Monday.
Both Quinn and Durbin said the possibility of selling the prison to the federal government was a once-in-a-lifetime opportunity to help create about 3,000 jobs, both at the prison and directly in surrounding communities in an area where unemployment has topped 10 percent.
"We have an opportunity to bring thousands of good-paying jobs to Illinois when we need them the most," Durbin said at a news conference in Chicago, one of several Illinois stops Sunday. "We have an opportunity to bring them to a part of our state that has been struggling and that's an opportunity we are not going to miss."
Critics, including Republican members of Congress from Illinois and GOP candidates for governor, have been quick to condemn the prospect of the sale because of safety concerns.
GOP gubernatorial candidate Andy McKenna said Quinn's plan to cut spending and create jobs includes bringing "terrorists to Illinois."
"I wholeheartedly oppose Governor Quinn and President Obama's efforts to move Gitmo detainees to our neighborhoods," McKenna said in a statement.
The plan to consider using the Thomson facility was first reported by the Chicago Tribune.
Thomson has been largely vacant since its construction in 2001 because of budget problems. The prison was built with 1,600 cells, but only about 200 minimum security inmates are held there. Durbin brushed off security concerns, saying convicted terrorists are already incarcerated in federal prisons without incident.
He said fewer than 100 of the inmates at Thomson would be Guantanamo Bay detainees if the Federal Bureau of Prisons buys the facility. Federal officials would even erect a more secure perimeter around the prison to beef up security, he added.
"We're here today to let the people know we're not going to let the fearmongers carry the day," Quinn said. "We're going to do things right, the Illinois way."
President Barack Obama's administration wants to close Guantanamo Bay, a military run detention center in Cuba, and move the detainees to the U.S. so they can be prosecuted for their suspected crimes.
The detainees are alleged terrorism suspects who have been held often without charges since the beginning of the war in Afghanistan.
Local and state officials will be at Thomson on Monday for an inspection by the Federal Bureau of Prisons and Department of Defense representatives.
U.S. Rep. Donald Manzullo, a Republican whose district includes Thomson Correctional Center, was invited to Monday's meeting with federal officials at the prison but he did not plan to attend, his spokesman Rich Carter said Sunday.
Manzullo said he adamantly opposes the proposal, despite the jobs it would bring to the area.
Federal officials were considering Thomson along with a facility in Florence, Colorado and a site in Hardin, Montana.
Some 215 detainees remain at Guantanamo Bay, and Durbin says the administration has talked to other countries about taking some of them. Durbin said he didn't know when the Obama administration would decide, but hoped Illinois would have an advantage because of Obama's connection to the state.
"He understands this part of our state, he knows the state of the economy there," Durbin said.
Quinn said he talked to Obama about a prison deal regarding Thomson during a recent trip to Washington.
Jack Lavin, a top aide to Quinn, said Quinn does not need legislative approval to sell the prison property. But the legislature would get involved when it comes to awarding jurisdiction if it becomes a federal prison.
Thomson Village Board President Jerry Hebeler lobbied Quinn to consider selling the prison to the federal government to help rejuvenate the area that has suffered because the prison never fully opened.
"After eight years of living in limbo, we are open to any and all alternatives," Hebeler said.
Reaction from some residents of the tiny village of about 500 people, has been generally positive.
Craig Mathers, superintendent of the West Carroll School District, which includes Thomson, attended a candidate forum where Quinn was speaking Sunday so that he could get more information. "I'm not too worried about safety and security because it was built as a maximum-security prison," Mathers said. "I'm more concerned about whether to prepare for an additional 250 students showing up on my doorstep next August."
Associated Press Writers Sophia Tareen in Chicago and Christopher Wills in Rockford, Ill., contributed to this story.