The foreign secretary and the chancellor have authorised government lawyers to examine how to settle a 38-year-long dispute, according to reports.
The money is part of a payment of £650 million made by Iran in the 1970s to buy 1,500 Chieftain tanks from Britain and fix 250 more.
Zaghari-Ratcliffe's husband, Richard Ratcliffe, met with Johnson on Tuesday and asked him to secure him a safe passage to Iran.
She is now serving a five-year jail sentence for alleged sedition, and has been threatened with further charges and a new trial that could double her sentence. The UK was ordered to repay the debt in 2009 by the International Chamber of Commerce but United Nations and European Union sanctions levied against Iran prevented the repayment.More news: President Trump tweets and then deletes message about Sutherland Springs shooting
A spokesman for Britain's Foreign Office could not be reached for comment out of normal business hours but Senior Whitehall sources have told the The Telegraph that the payment is not directly linked to the fate of Zaghari-Ratcliffe and that work has intensified in recent months in a bid to improve relations with Iran. However Westminster continues to insist that the two issues are unrelated.
But the section of the Iranian government owed the money - the Ministry of Defence and Support for Armed Forces Logistics (MODSAF) - continues to be listed as one of the organisations that remains the subject of worldwide sanctions despite the deal, the i has found. It added: "This is a longstanding case and relates to contracts signed over 40 years ago with the pre-revolution Iranian regime". "It is wrong to link a completely separate debt issue with any other aspect of our bilateral relationship with Iran". The government said lawyers would discuss the issue, but said the question was whether it would help her case. Zaghari-Radcliffe is entitled diplomatic protection but Johnson said "it is a big step". Ratcliffe said he hoped Johnson, who will travel to Iran within the next few weeks, will bring his wife home in time for Christmas.
Zaghari-Ratcliffe is said to be close to a nervous breakdown.