The UAE’s ambassador in London is due to issue a statement at 10:00 GMT, amid speculation he will talk about progress in the 31-year-old’s situation.
On Thursday, Foreign Secretary Jeremy Hunt said he had “constructive” talks with his opposite number in the UAE.
Hedges, of Durham University, was jailed for life but denies spying.
His wife, Daniela Tejada, who arrived back from the UAE on Thursday morning, said Mr Hunt had assured her he was doing all he could when they met at the Foreign Office.
And BBC diplomatic correspondent Paul Adams tweeted that things were “looking a bit more positive” for Hedges, with Foreign Office sources suggesting there had been an “olive branch” from the Emirati foreign minister.
“The UAE may feel that having allowed the legal process to run its course, the time has now come to show magnanimity and not risk a very real diplomatic breakdown with a close, important ally,” he added.
On Thursday evening, Mr Hunt tweeted he had “just had a constructive conversation with UAE Foreign Minister Sheikh Abdullah bin Zayed”.
“I believe and trust he’s working hard to resolve the situation asap,” he posted.
“We’ve a close partnership with UAE which will help us take things forward.”
Mr Hunt met Ms Tejada in the wake of her criticism of the UK government for failing to take a firm enough stance with the UAE.
However, speaking afterwards, Ms Tejada thanked the foreign secretary for “taking the time” to meet her at “this crucial point”.
“He has assured me that he and his team are doing everything in their power to get Matt free and return him home to me,” she said.
“This is not a fight I can win alone and I thank the Foreign Office and the British public for now standing up for one of their citizens.”
Political scientist Hedges, who is originally from Exeter, had been in the country conducting research on the UAE’s security strategy for his PhD thesis when he was arrested at Dubai airport.
Prosecutors said he had confessed to spying.
The UAE Ministry of Foreign Affairs said the country was “determined to protect its important strategic relationship with a key ally” and added it hoped both sides could find “an amicable solution” to the case.
The country’s Attorney General Dr Hamad Saif Al Shamsi previously said Hedges had the right to appeal.
Abdulla Al Naqbi, head of the ministry’s Department of Legal Affairs, had said that “families also have the right to appeal for presidential clemency on behalf of convicted relatives”.
In a statement, Mr Al Naqbi said “compelling and powerful evidence was presented in court” and that this included Mr Hedges’ own confession.
Hedges was offered, and accepted, the services of a court-appointed lawyer and was also provided with translators, he said.
“It is not true that he was asked to sign documents he did not understand,” Mr Al Naqbi said.