Nazanin Zaghari-Ratcliffe could be back in Britain within weeks, after the UK government intensified talks with Iran to secure her release.
The Iranian-British woman was arrested in 2016 and jailed on charges of sedition. Her detention period is due to expire on March 7, but the UK government is hoping for an earlier release.
"We have intensified those negotiations and are leaving no stone unturned, and I want to get Nazanin released, absolutely as soon as possible," UK Foreign Minister Dominic Raab told Sky News on Sunday.
He urged caution, however, stressing that Iran had repeatedly dashed hopes of a release.
Mr Raab said owing to the inauguration this week of Joe Biden's US administration, the "contours and the thinking" in Iran may change, and there may be "additional possibilities".
His comments were welcomed by Ms Zaghari-Ratcliffe's husband Richard Ratcliffe, who has campaigned for her release for five years.
"We haven't yet had a response from the Iranian embassy to our family's attempts to discuss with them the arrangements for Nazanin's release, which is not a great sign," Mr Ratcliffe said. "But Nazanin is remaining hopeful."
Unanswered questions include whether she will fly home on a military or passenger plane, whether her electronic ankle tag will be removed, and how she will retrieve her passport.
Ms Zaghari-Ratcliffe, 43, worked for the charity arm of Thomson Reuters Foundation when in April 2016 she was arrested at Iran's Tehran airport.
Five months later, she was sentenced to five years' imprisonment after being found guilty of plotting to topple the Iranian government.
Both her family and the UK government have repeatedly said that Tehran is using her as a pawn in its dispute with Britain over an unpaid £400 million bill for 1,500 tanks dating to 1979. Ms Zaghari-Ratcliffe has previously questioned the decision not to repay the debt.
She was released from Evin prison last year as the coronavirus swept through, and has since been living under house arrest at her parents' home in Tehran.
There, she has turned to author Lewis Carroll's most famous work for solace, said her husband.
He said that she had made a seven-week wall calendar using Alice in Wonderland notepaper to count down the weeks, with the last week marked "freedom".
If she were to be freed on that date, it would mark the realisation of a Christmas wish. In December, her daughter wrote to UK Prime Minister Boris Johnson seeking to have her mother returned. This video has the story.