Negotiations with Iran to free Nazanin Zaghari-Ratcliffe are "going right up to the wire", the Prime Minister said while visiting Abu Dhabi.
The mother-of-one, who holds duel British-Iranian citizenship, has been detained in Iran for almost seven years on charges of plotting against the regime.
On Tuesday she was handed back her British passport raising fresh hopes she could be released within days.
Mrs Zaghari-Ratcliffe’s lawyer also said he was “hopeful” there would be good news soon, as Tehran and London pressed on with talks about a long-standing debt.
Her imprisonment has been linked to a £400 million historic debt that Britain owes Iran.
On Wednesday Foreign secretary Liz Truss said the UK is determined to pay the “legitimate debt that we do owe Iran” despite the Iranian regime being under sanctions.
She said the UK was working “very hard” to “secure the release of Nazanin“, and other dual-nationals Anoosheh Ashoori and Morad Tahbaz.
Ms Truss said she cannot say “anymore at this stage”, but those imprisoned in Iran had “been through an appalling ordeal and we want to secure their release as soon as possible”.
Earlier, Boris Johnson said talks with Iran were "moving forward" but that he could not say more as "negotiations continue to be under way".
Asked by broadcasters at the Emirates Palace hotel in Abu Dhabi whether a UK negotiating team was currently in Tehran, the Prime Minister said: "It is true and it has been for a long time that we're negotiating for the release of our dual nationals in Tehran.
"There are some very sad cases, including Nazanin.
"I really don't think I should say much more, I'm sorry, although things are moving forward.
"I shouldn't really say much more right now just because those negotiations continue to be under way and we're going right up to the wire."
Labour MP Tulip Siddiq on Tuesday posted a picture with Mrs Zaghari-Ratcliffe’s husband, Richard Ratcliffe, and said: “Her husband Richard and I met earlier today for yet another strategy meeting… hopefully not many more!!”
On Wednesday morning, she said Mrs Zaghari-Ratcliffe’s family were feeling "more hopeful".
Thank you all ever so much for such kind messages about my constituent Nazanin Zaghari-Ratcliffe. It’s so heartwarming to see the affection for her.
— Tulip Siddiq (@TulipSiddiq) March 15, 2022
Her husband Richard and I met earlier today for yet another strategy meeting… hopefully not many more!! #FreeNazanin pic.twitter.com/iAgm5YrkN3
The Hampstead and Kilburn MP told BBC Breakfast: "As you can imagine, (her husband) Richard is feeling hopeful, more hopeful than he has in six years. You know, this campaign has been very long. It feels like there's a bit of light at the end of a very long tunnel."
She said Mrs Zaghari-Ratcliffe had been called in for "quite intense" questioning by the Iranian Revolutionary Guards and the Ministry of Intelligence and then had her British passport returned - for the first time since April 3, 2016.
Ms Siddiq added: "She is technically on a travel ban but the fact that a passport has been given to her makes us feel very hopeful, and her husband is certainly feeling quite hopeful today."
Iranian media has reported that the UK has settled the £400 million it owes the country over the non-delivery of Chieftain tanks in 1979.
However, Iranian Government officials did not comment when asked whether the amount had been paid, Reuters news agency said.
The Foreign Office refused to confirm whether it had settled the debt with Iran or if it expected Mrs Zaghari-Ratcliffe to be released.
