The UAE's ambassador in London, Sulaiman Almazroui, added to the mood of optimism when he said they were hoping for an "amicable solution".
But Matthew's wife Daniela Tejada said he remains terrified that he will have to serve the full life sentence which was handed down when he was convicted of spying.
She had a five-minute phone call with him on Thursday night and said: "He is not well.
"He mentioned that his panic attacks have become worse than they were before. However, he did say that he has access to a doctor.
"I wasn't allowed to know where he is, so still don't know anything about his whereabouts, and I think he's just absolutely terrified at the idea of having to spend the rest of his life behind bars for an offence he hasn't committed."
Matthew, a Middle Eastern studies specialist visited the UAE to research his Durham University PhD thesis on the Gulf state's security policies following the Arab spring.
He quizzed locals about their country's foreign policy before he was arrested at Dubai Airport on May 5 as he prepared to fly home.
He was held in solitary confinement for more than five months before being convicted of spying for the UK government at a hearing where he had no legal representation. Foreign journalists were barred from the hearing.
Mr Almazroui tried to defend his country's judicial system and said: "Over the course of one month, three judges evaluated compelling evidence in three hearings.
"They reached their conclusions after a full and proper process. This was an extremely serious case.
"We live in a dangerous neighbourhood and national security must be a top priority." But Colombian-born Daniela, who met Matthew when they were both studying at Exeter University, dismissed his claims.
She said: "The judicial system in the UAE and the UK cannot be compared.
We have asked for clemency, we will wait to see what happens." Professor Stuart Corbridge, vice-Chancellor of Durham University, said: "There is no reason to believe that Matt was conducting anything other than legitimate academic research." Mr Hedges was given 30 days to challenge the court ruling.
Daniela has launched a petition on Change.org demanding his release where she says: "These charges are absurd. I am desperately pleading for help to get the charges dropped, and bring him home to the UK, where he belongs." Nearly 200,000 had signed the petition by yesterday.
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