The channel reported that deals have been reached to release prisoners with Western ties held in Iran.
The official also said a deal with the US will see a prisoner swap in exchange for the release of 7 billion dollars (£5 billion) in frozen Iranian funds.
Mrs Zaghari-Ratcliffe will be released “after the payment of a military debt” the broadcaster said.
UK officials have downplayed the prospect of Mrs Zaghari-Ratcliffe’s imminent release.
Her husband Richard Ratcliffe said the family had not been updated.
The Foreign Office said “legal discussions are ongoing” and that government’s position had not changed over the weekend.
They added that Iran had made the claim before without the mother having been released.
Mr Ratcliffe, who has campaigned for the release of his wife after her detention in 2016, said: “We’ve heard nothing.”
Earlier, the Foreign Secretary said the treatment of Mrs Zaghari-Ratcliffe by Iran amounts to “torture” and accepted she is effectively being held hostage by the Middle Eastern state.
Dominic Raab told the BBC’s The Andrew Marr Show she was being “subjected to a cat and mouse game” by the Iranians.
Asked if she could be described as a hostage, he replied: “I think it’s very difficult to argue against that characterisation.
“It is clear that she is subjected to a cat and mouse game that the Iranians, or certainly part of the Iranian system, engage with and they try and use her for leverage on the UK.”
The British-Iranian dual national was sentenced to a fresh jail term of one year on Monday and handed a year-long travel ban in Iran on a new charge of “spreading propaganda against the regime”.
She has already served a five-year prison sentence after being detained on charges relating to national security in 2016.
The mother-of-one, who lived in north London before her arrest, was detained at Tehran airport after travelling to Iran to introduce her daughter to her parents.
She and her family believe she is being held as political leverage to try to force the UK’s hand in a long-running financial dispute between the UK and Iran.
It dates back to the 1970s when the then-shah of Iran paid the UK £400 million for 1,500 Chieftain tanks.
When the shah was toppled in 1979, Britain refused to deliver the tanks to the new Islamic Republic but kept the cash, despite British courts accepting it should be repaid.
Asked about the debt on Sunday, Mr Raab said: “It’s not solely about that.
“That is not actually the thing that’s holding us up at the moment, it’s the wider context as we come up to the Iranian presidential elections and the wider elections on the JCPOA (Joint Comprehensive Plan of Action) which, inevitably from the Iranian perspective, the two are considered in tandem.
“Nazanin is held unlawfully, in my view, as a matter of international law. I think she’s being treated in the most abusive, tortuous way. I think it amounts to torture, the way she’s being treated.”
On Tuesday, Mr Ratcliffe said ministers were “enabling the abuse” his wife has suffered through their “reluctance to do anything” that might upset Tehran.
He urged the Government to target members of Iran’s leadership with new Magnitsky sanctions, which focus on people involved in some of the gravest human rights abuses around the world.
“I think that’s proportionate, that is not extreme – these guys need to feel that this is a bad tactic,” he added.
Mr Ratcliffe, commenting on the lack of British representation in court at his wife’s most recent hearing, said: “What we got told was that they (the UK Government) didn’t want to do something provocative that could could cause harm to Nazanin.
I am aware there are news reports circulating about the debt being paid to #FreeNazanin. I have spoken to her family and they have heard nothing confirming any of these rumours.
— Tulip Siddiq (@TulipSiddiq) May 2, 2021
“And I was like, ‘Are you effing kidding me?’ You either stand up and protect her or you allow it to happen.
“They are taking her to court for the second time on a second stage of nonsense when you’ve invoked diplomatic protection – you need to show that your protection should be taken seriously.
“And the failure to do that will have emboldened the Revolutionary Guards to follow through and give her the sentence – and they gave the maximum they could.
“The timidity of the Government will have been a contributing factor.”
The report in Iran raised the prospect that there was co-ordinated action between Tehran, London and Washington.
Last Monday, Prime Minister Boris Johnson acknowledged “we are working with our American friends on this issue”.
Labour MP Tulip Siddiq, who represents Mrs Zaghari-Ratcliffe’s constituency of Hampstead and Kilburn, said her family were not getting their hopes up over her possible release.
She told Sky News: “There’s just been one failure after another on the part of the government to release her and bring her back home, so (her family) are not being too hopeful when I’ve spoken to them.”
Lydia Parker, of Amnesty International UK, said: “It’s extremely unclear what is actually happening.
“We sincerely hope this isn’t just more cruel games from the Iranian authorities.
“If this is indeed a sign that the end is in sight, we once again call on the UK Government to intervene as forcefully as possible to ensure that Nazanin is released at the earliest possible moment.
“This won’t be over until Nazanin has her passport in her hand and is sitting on a flight back to Britain.”