Radical cleric Abu Qatada has volunteered to leave Britain if a treaty between the UK and Jordan on the use of evidence obtained by torture is ratified.
The agreement, unveiled by the Home Secretary last month, aims to allay fears that evidence extracted through torture will be used against the terror suspect at a retrial.
The British Government has been trying to deport Qatada to Jordan, where he was convicted of terror charges in his absence in 1999, for nearly eight years.
ITV News Correspondent Juliet Bremner reports:
Qatada, also known as Omar Othman, must wait to learn if he can be released from jail after his bail application at an immigration tribunal was adjourned to May 20.
At the Special Immigration Appeals Commission, Qatada's lawyer Edward Fitzgerald QC said, "If and when the Jordanian parliament ratifies the treaty, Mr Othman will voluntarily return to Jordan".
Prime Minister David Cameron said he will be "one of the happiest people in Britain" if Abu Qatada returns to Jordan of his own accord.
The Home Office said Theresa May's focus remains seeing Qatada returned to Jordan "at the earliest opportunity":
Shadow Home Secretary Yvette Cooper said this could be "very good news" if he returns to Jordan "as soon as possible".
"Abu Qatada should have made this decision a long time ago as this legal process has dragged on far too long. We will watch the next steps closely until he departs, but I hope this saga can now be brought to an end," Ms Cooper added.