Kellie Hamill, who has been pleading in the media for her husband's release, said Jackson made the offer last week and she asked him to intervene.
"We talked with him several days ago," she said in a telephone interview from the couple's home in Macon.
U.S. Sen. Trent Lott (search) said Friday at a news conference in Tupelo he had talked with Jackson and helped the longtime civil rights advocate contact the Hamill family.
Lott said one step Jackson wanted to take was to write a letter to Al-Jazeera, the Arabic language television network, and encourage Hamill's release.
There was no immediate response to messages seeking comment from Jackson's Rainbow/PUSH coalition in Chicago on Saturday, and it was unclear if he had already sent the letter or taken other steps.
Thomas Hamill, 43, a fuel tanker driver for Halliburton Co. subsidiary Kellogg, Brown & Root, was abducted April 9 when gunmen attacked his convoy.
Jackson has been instrumental in securing the release of other American hostages.
In 1990, during the first Gulf War (search), Jackson negotiated the release of Americans held hostage in Kuwait and Iraq. In 1999, he helped secure the release of U.S. soldiers held hostage in Kosovo (search).
In a statement issued Thursday, Jackson appealed both to Hamill's captors and to religious leaders in Iraq.
"Mr. Hamill came to Iraq not to wage war against any group or religion, but to serve the Iraqi people and thus help relieve their pain and sufferings," Jackson said in the statement that also called for the release of other hostages.
Kellie Hamill was awaiting the results of tests to determine whether four bodies discovered west of Baghdad earlier in the week are the remains of civilian U.S. contractors missing since the assault on their convoy.
Nightly vigils and prayer meetings have been held in Macon since Hamill was abducted.