In a statement released by the UK Foreign and Commonwealth Office, Barbara Henning said in a message to the IS: "We are at a loss why those leading Islamic State cannot open their hearts and minds to the facts surrounding Alan's imprisonment and why they continue to ignore our pleas for dialogue."
Details of the message to his wife from the 47-year-old Henning, who was transporting humanitarian aid shipments when abducted in December 2013, were not disclosed.
"We have seen Muslims across the globe question Islamic State over Alan's fate. The voices of the people have spoken out loud and clear," she said.
The IS militants threatened to kill Henning in a video released Sep 13, which also showed the beheading of Briton David Haines, whose death followed the beheadings of American journalists James Foley and Steven Sotloff, also shown in videos released by the group.
"Alan was working with Muslims to help the most vulnerable within Syria. Nothing has changed. He went to Syria to help his Muslim friends deliver much-needed aid," his wife said.
"I have been told that he has been to a Sharia Court and found innocent of being a spy and declared to be no threat. I implore Islamic State to abide by the decisions of their own justice system. Please release Alan," she pleaded.
On Tuesday, the IS released a second video of British journalist hostage John Cantlie, abducted in Syria in 2012.