The Foreign Secretary will travel to Tehran in a bid to win the release of the jailed Iranian-British aid worker, the Guardian newspaper reported.
Mrs Zaghari-Ratcliffe is serving a five-year sentence over allegations of plotting to overthrow the Tehran government, having been arrested in 2016 during a holiday visit to show her baby daughter Gabriella to her parents.
She is facing a further court appearance this month, following threats to increase her sentence by five years as a result of a gaffe by Mr Johnson.
Mrs Zaghari-Ratcliffe, a project manager with the Thomson Reuters Foundation, denies the charges.
Her fate became a major political issue in Britain after Mr Johnson made remarks on November 1 that appeared to cast doubt on statements from her employer about what she had been doing in Iran.
The Foreign Secretary wrongly told a parliamentary committee that she had been in Iran to train journalists. He later acknowledged that this was not the case.
The Thomson Reuters Foundation, a charity organisation that is independent of Thomson Reuters and operates independently of Reuters News, said she had been on holiday.
The Foreign Office refused to confirm the trip.