Kirk, 52, of Highland Park, Ill., underwent three surgeries and is expected to regain his mental faculties but could suffer lasting paralysis on his left side, doctors have said. He is being treated at the Rehabilitation Institute of Chicago.
U.S. Rep. Judy Biggert and former U.S. Rep. John Porter say they are anxious to visit Kirk once staffers say he's available, the Chicago Tribune reported.
Kirk's staff is releasing little information about the senator's recovery.
"We have made it clear that there will not be interviews done at this time. To be more clear: There will be no interviews done at this time by the senator, his staff, his family or the hospitals," Kirk's deputy chief of staff, Kate Dickens, said in an e-mail to the Tribune.
Kirk has been hospitalized since Jan. 21 when he suffered an ischemic stroke,
The last update provided on the senator's Web site was posted Feb. 17.
At that time, Dr. Richard L. Harvey, medical director of the Rehabilitation Institute of Chicago, said Kirk was adapting well to the rehabilitation program and had started walking exercises on a treadmill.
A neurologist at Johns Hopkins Medicine in Baltimore told the Tribune the decision to restrict visitors may be due to public relations considerations if the senator is suffering impairments such as slurred speech.