Nazanin Zaghari-Ratcliffe, who has been held in an Iranian jail for more than 18 months, is eligible for early release.
Mrs Zaghari-Ratcliffe told her husband Richard that she had been informed of the news by her Iranian lawyer.
Her case has been marked on the Iranian judiciary database as "eligible for early release".
Richard Ratcliffe said he was "cautious" about the news but hoped his wife, who was arrested in 2016 during a holiday, would be home soon.
He told Sky News: "It is definitely a positive step. I'm probably a bit cautious to see just how positive.
"There has not been any confirmation to her from the prosecutor so, what she got told, there is still some paperwork to finalise, so hopefully by Christmas, but Christmas is not very far away at all.
"But it's definitely good news and fingers crossed now."
He said since Foreign Secretary Boris Johnson's visit to Iran early in December there had been "incremental improvement" in her case, including allowing her more phone calls.
He added: "I think it feels like the tide has turned, certainly."
Mr Ratcliffe said that once his wife was home there would have to be "lessons learned but that's for another day".
Mrs Zaghari-Ratcliffe, who is British-Iranian, was arrested at the airport in Tehran after visiting her family with her daughter in 2016.
She is serving five years in prison after being charged with planning to topple the Iranian government, which she denies.
Mr Johnson met with Iranian Foreign Minister Mohammed Javad Zarif in Tehran earlier this month to discuss Mrs Zaghari-Ratcliffe's case.
Before his intervention, Mr Johnson was forced to apologise after he said he had understood she was "teaching journalists" while in Iran.
Authorities used this as justification for new charges against her of "spreading propaganda".
Mrs Zaghari-Ratcliffe's husband has previously said she could face another 16 years in prison as a result of the Foreign Secretary's gaffe, which Mr Johnson apologised for.
The family's hopes were heightened when she was due to go on trial at the beginning of December but this did not go ahead.
At the time Mr Ratcliffe said it offered a "ripple of freedom".
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