Nazanin Zaghari-Ratcliffe has been given her British passport back while detained in Iran, raising fresh hopes she could be freed.
Her MP Tulip Siddiq has said she understands there is a British negotiating team in Tehran where the mother-of-one is being detained.
Mrs Zaghari-Ratcliffe is a British-Iranian citizen who has been detained in Iran since 2016.
She was arrested while visiting her parents and accused of crimes against national security.
It was alleged that she was running a journalism course that encouraged people to spread propaganda.
According to her family, she was told by Iranian authorities that she was being detained because of the UK's failure to pay an outstanding £400 million debt to Iran.
The United Nations has called for her release, and 1.5 million people signed an online petition urging British and Iranian leaders to secure her safe return to the UK.
This morning Tulip Siddiq, here Hampstead and Kilburn MP tweeted: "I am very pleased to say that Nazanin Zaghari-Ratcliffe has been given her British passport back.
"She is still at her family home in Tehran. I also understand that there is a British negotiating team in Tehran right now.
"I will keep posting updates as I get them."
No10 refused to comment on whether Mrs Zaghari-Ratcliffe is set to be released or whether the UK has a negotiating team in Iran.
Downing Street said the UK is “committed to paying” the £400m debt to Iran, but “we’ve always been clear it’s not linked” to Mrs Zaghari-Ratcliffe’s case.
At the end of last year, Mrs Zaghari-Ratcliffe's husband Richard went on hungers strike outside the Foreign Office in London.
Richard Ratcliffe has said that the government "only deals with problems when they become crises", and has been heavily critical of its response to the family's plight.
He called on Prime Minister Boris Johnson to acknowledge that his wife is being held "hostage" in Iran, and has pitched a tent in central London where he plans to keep a vigil outside the government building.
His protest was also designed to shine a light on the plight of other UK nations arbitrarily held in Iran, including Anoosheh Ashoori, Mehran Raoof and Morad Tahbaz.
Mr Ratcliff ended his hunger strike after 21 days.
At the time he said his job was to "keep going", adding: "We probably hoped we'd get a breakthrough doing this. We haven't yet.
"I didn't want to go out in an ambulance. I want to walk out with my head held high."
In January, the daughter of another British-Iranian detained in Iran said her father was to begin a hunger strike due to a lack of progress in securing his release.
Retired civil engineer Anoosheh Ashoori has been held at Evin Prison on charges of spying for Israel, which he denies, for more than four years.
In a video posted in relation to the hunger strike, Elika Ashoori said she was at that time "extremely concerned" for her father's health "as he approaches his 68th birthday".
In December, Foreign Secretary Liz Truss said the £400 million that Britain owes Iran is a "legitimate debt" that the Government wants to pay.
Amnesty International said “the time for promises is over”, calling on the government to set out a strategy to secure the release of British nationals detained in Iran.
Sacha Deshmukh, Amnesty International UK's chief executive, warned that the latest reports should be treated with caution as there had been "false dawn after false dawn" in the long-running process.
He said: "We sincerely hope these reports are correct.
"The detainees and their families have been suffering for years, and a resolution can't come quickly enough.
"It's been clear for a long time that the Iranian authorities have been targeting foreign nationals with spurious national security-related charges to exert diplomatic pressure.
"In the past we've had false dawn after false dawn over possible breakthroughs, so it's only right to be cautious at the moment."
