Richard Ratcliffe said his wife’s father had been told her two-week furlough had been extended until 18 April.
Her file has also been put forward to the Iranian Prosecutor General to be considered for clemency, he added.
Ms Zaghari-Ratcliffe was arrested at Tehran’s Imam Khomeini airport in April 2016 while travelling to show her young daughter, Gabriella, to her parents.
The aid worker, from Hampstead, in north London, was sentenced to five years in prison over allegations, which she denies, of plotting to overthrow the Tehran government.
Ms Zaghari-Ratcliffe was later given diplomatic protection by the UK government, which argues that she is innocent and that her treatment by Iran failed to meet obligations under international law.
She has been living at her parents’ house in Tehran since her temporary release but must wear an ankle tag and must stay within 300 metres of the property.
Former foreign secretary Jeremy Hunt welcomed the latest development in her case as a “glimmer of hope amidst the darkness”.
“Let’s pray that this remarkable family are reunited soon,” he wrote on Twitter.
The family’s MP Tulip Siddiq tweeted that every day Mrs Zaghari-Ratcliffe is out of prison is “better than the alternative”.
But she said that the main focus remained “getting her home and away from the danger of coronavirus in Iran as soon as possible”.
Iran is among the countries worst-affected by Covid-19 – reporting over 29,000 confirmed cases and more than 2,200 deaths from the disease.
Additional reporting by Press Association.