Mr Johnson has faced calls to resign after telling a Commons Committee some weeks ago that Nazanin Zaghari Ratcliffe had been in Iran "training journalists".
A Foreign Office statement said the pair will meet to discuss Mr Ratcliffe's request to give his wife "diplomatic protection" - which, under global law, allows a state to take diplomatic action on behalf of a national.
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 worldwide law, allows a state to take diplomatic action on behalf of a national.
Iranian-British aid worker Nazanin Zaghari-Ratcliffe is seen in an undated photograph handed out by her family.
"I reject any suggestion that she was there in a professional capacity", he said.
She claimed his recent comments to the foreign affairs select committee had made Mrs Zaghari-Ratcliffe's situation worse by suggesting that she had been there to train journalists. She has been accused of working with the company and her previous employer, the BBC, to overthrow the Iranian government.
Responding to Labour's initial question, Mr Johnson earlier outlined the circumstances of Mrs Zaghari-Ratcliffe's arrest before adding the UK Government has "no doubt" she was in Iran on holiday.
He will speak to the Foreign Secretary at the Foreign Office at 10am, in a bid to help secure his wife's release from Iran.
The Foreign Secretary told MPs on Monday there were "overwhelming" humanitarian grounds for her release and stressed that she was in Iran on holiday. There are also fears she is developing cancer after finding lumps in her breasts.
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 was arrested by Iran's Revolutionary guard in April 2016 as she tried to return home to London with her 21-month-old daughter Gabriella after a two-week holiday. Her mood has become uncontrollable.
The family's local MP Tulip Siddiq told Sky News that Mrs Zaghari-Ratcliffe had sobbed inconsolably during an earlier phone call with her husband, saying: 'She just said that she couldn't believe that Boris Johnson would make those comments. This is a young mother who could die if the Foreign Secretary doesn't retract his comments promptly, if he doesn't go to Iran and get her back'.