Also at the meeting in the Foreign and Commonwealth Office in London was Middle East minister Alistair Burt, who has met Mr Ratcliffe before and visited Mrs Zaghari-Ratcliffe's family in Tehran, and FCO consular officials who have been providing support to the family.
She was sentenced to five years after being convicted by an Iranian court of plotting to overthrow the Islamic Republic's clerical establishment.
Answering an urgent question in parliament, the Foreign Secretary also played down suggestions that the United Kingdom could give diplomatic status to Nazanin Zaghari-Ratcliffe, who was arrested 19 months ago when she was on holiday visiting relatives in Iran and subsequently imprisoned.
The Foreign Secretary has faced calls to resign over claims that Nazanin Zaghari-Ratcliffe could have her jail time increased after he wrongly said she had gone to the country to train journalists.
A Foreign Office statement to the BBC said Johnson and Ratcliffe will meet to discuss a request to give Zaghari-Ratcliffe "diplomatic protection" - which, under global law, allows a state to take diplomatic action on behalf of a national.
He said he would discuss the idea of giving Mrs Zaghari-Ratcliffe diplomatic protection in a meeting with her husband this week.
Zaghari-Ratcliffe is said to be close to a nervous breakdown.
Britain's Johnson to meet husband of aid worker jailed in Iran
Yesterday, Mr Ratcliffe said he had had a "positive" 20-minute phone call with Mr Johnson, in which the Foreign Secretary had promised to meet him within the next few days.
Her husband has campaigned for her release, insisting she was on holiday with their 18-month-old daughter Gabriella so the child could meet her grandparents in Iran.
The meeting will also discuss concerns about Mrs Zaghari-Ratcliffe's health and Mr Johnson's plan to travel to Iran before the end of the year.
The Foreign Secretary has sought advice from officials to determine whether conferring the status would help, including what impact it would have on the support now being provided and the representations already being made on Mrs Zaghari-Ratcliffe's behalf.
Nazanin Zaghari-Ratcliffe has been held by Tehran since April 2016 after being accused of spying - charges she denies.
Mr Ratcliffe said Mr Johnson had told him he was "deeply sorry for Nazanin's suffering", but did not say if the Foreign Secretary had made a personal apology for his blunder. "The government will continue to do this in the way that we judge is in their best interests, and the foreign secretary has made it clear that no stone should be left unturned".
Boeing gets $27 billion order from Middle Eastern airline
Egyptair could announce indirect orders with Airbus and Boeing involving third parties, they added. The rest of the initial order will be made up of the MAX 8 and MAX 9.