Mohammad Hjuj told AFP he was among a group of MPs who met last Monday the Jordanian cleric in jail.
"He told us that Tunisia offered him asylum before he was deported to Jordan ," said Hjuj, a member of a parliamentary committee on freedoms.
"Abu Qatada said he refused the offer because he wanted to return to Jordan after (receiving) government guarantees related to his trial," Hjuj said without giving details about the offer.
"He told us that all what he cared about was to return home and have a fair trial because he believes he is innocent," Hjuj said.
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Abu Qatada is jailed in the Muwaqqar prison, a maximum security facility in the desert east of Amman that houses more than 1,000 inmates most of whom are Islamists convicted of terror offences.
He was condemned to death in absentia in 1999 for conspiracy to carry out terror attacks, including on the American school in Amman, but under Jordanian law is allowed a retrial with him present in the dock.
Yesterday, a military court rejected a bail application by Abu Qatada, who was born Omar Mahmud Mohammed Otman in Bethlehem in the now Israeli-occupied West Bank, which was in Jordan at the time of his birth.
"I think the state should deal with Abu Qatada in a special manner because he is a leader of a group that has weight worldwide," said Hjuj.
"I did not feel Abu Qatada was radical or extremist during the meeting. We had an open and deep talk. He is not like others who considered us atheists and refused to meet with us."