The decision, which would escalate her case from a consular issue to a state matter and could be used to apply further pressure on Tehran to release her, was sitting on Johnson's desk before his resignation.
"What the Foreign Office told us is that it's going to take some time and they would let us know when [the new foreign secretary] is ready to receive full application again. We were expecting a decision this week and we would not get that decision this week," her husband Richard Ratcliffe told The Guardian.
Zaghari-Ratcliffe, who works for the Thomson Reuters Foundation, is serving a five-year prison sentence for allegedly planning the "soft toppling" of Iran's government while traveling with her young daughter.
The young girl, Gabriella, has remained in Iran in the care of relatives.
The MP representing Zaghari-Ratcliffe on Tuesday demanded an urgent meeting with the new foreign secretary Jeremy Hunt.
Tulip Siddiq, MP for Hampstead and Kilburn, described Hunt's predecessor Boris Johnson's record as "one of failure".
He added that Johnson - who resigned as foreign minister on Monday - had "actively damaged" the case by wrongly claiming Zaghari-Ratcliffe was in Iran training journalists.
Last month, her husband said she now faces a new charge of "spreading propaganda against the regime".
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He added that "the judge told Nazanin to expect that there will likely be another conviction and sentence against her".
The case became highly politicised in December after Johnson mistakenly claimed Zaghari-Ratcliffe had been training journalists in Iran - something the Thomson Reuters Foundation and her family have strongly denied.
Iran has used Johnson's remarks to justify the new charges and it may have contributed to her lengthened sentence.
In a letter shared by BuzzFeed on Tuesday, Siddiq told Hunt: "The very minimum one expects from the Foreign Office is that it seeks to protect British citizens who are in distress abroad".
"Despite his welcome promise to 'leave no stone unturned' for my constituent – he failed to deliver any meaningful progress to secure her release".
Zaghari-Ratcliffe's case comes as London is considering repaying Tehran some £400 million ($529m) from a pre-1979 arms deal.
Observers say Hunt will need to be briefed on the whole portfolio and the file resubmitted before a decision on diplomatic protection is reached.
On Wednesday, Nazanin's husband Richard penned an op-ed in The Guardian saying that despite Johnson's blunders his family were "upset" by the resignation because the case had become "a high priority", "enough to make him travel to Iran".
"I still have a pile of painted stones in our flat made to symbolise Johnson's vow to leave 'no stone unturned'," he wrote.
Richard said he plans to give the new foreign secretary one of the stones as a reminder of his wife Nazanin's case.
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