Spanish-language daily HOY published on its Web site that the Illinois Democrat made the revelation at a meeting with the Chicago Tribune's editorial board, owner of the publication.
It said that Durbin, who has been a sponsor of the bill currently stalled in the Senate, said that at this time the wording of the announcement about the DREAM Act and deportations is being worked on.
The senator mentioned no dates, but said it will be soon, HOY said.
"I believe that if students are eligible for the DREAM Act, they should not be the target of deportations," the senator told reporters, adding that in a short time the Department of Homeland Security will make a very positive announcement in that regard.
He gave no details about the possible announcement, but groups that defend undocumented immigrants have demanded that Obama use his executive powers to stop deportations, particularly of young people who could benefit from the DREAM Act.
Obama was in Chicago on Wednesday for a combination 50th birthday party/star-studded fundraiser, an occasion at which he was applauded by the 2,500 guests when he said, ""We are a nation of immigrants. We want to welcome extraordinary talent to our shores and have a legal immigration system that works for everybody."