Two UK Muslim peers who are in Sudan to lobby for the release of a jailed British teacher are meeting the country's president.
The planned meeting has raised hopes that Gillian Gibbons, 54, may be released early.
Baroness Warsi and Lord Ahmed delayed their return to the UK after progress was made in negotiations.
Mrs Gibbons was jailed for 15 days after allowing her pupils to name a teddy bear Muhammad.
The BBC's Adam Mynott said the prospect of an early release "was becoming more likely with each passing minute".
The pair had planned to return on Monday morning, but Lady Warsi said that they would remain in the country for a third day of talks.
The jailing of Mrs Gibbons has led to an international outcry and has embarrassed the government.
But at the same time President Omar al-Bashir is under pressure from Sudanese hardliners to ensure Mrs Gibbons serves her full sentence.
There have even been calls for a retrial and for the sentence to be increased.
On Sunday, Lady Warsi said that while negotiations had been "difficult", there was "a huge amount of goodwill to try and secure an early release" for the teacher.
She declined to give details of who the pair would be meeting, or what was being discussed. "These are very delicate times and we are trying to be as responsible and restrained as possible.", she said.
Mrs Gibbons still has "warm things" to say about Sudan, Lady Warsi said after meeting her again on Sunday.
She added: "I understand the cultural and religious sensitivities around Islam, but as a woman and a British woman I have huge concerns for Gillian and I just hope that we can carry on presenting the case for Gillian and reach an early resolution.
"This is a very important issue, a huge issue, and we must remain optimistic and hopeful that we can resolve it as early as possible."
She added: "They've presented us with hope. Enough for us to carry on having those meetings."
Mrs Gibbons's local MP Louise Ellman said: "I think it is a matter of doing everything that is possible, doing it very carefully, keeping very focussed and just dealing with things as they arise."
Following an hour-long visit to Mrs Gibbons by the British ambassador on Sunday, a Foreign Office spokesman said: "Government ministers and officials in London and Sudan are continuing to do everything they can to try to resolve this consular issue as quickly as possible through intense activity on a wide range of channels."
The two peers have already held meetings with Sudanese government officials, including the foreign minister, to try to resolve the situation.
Mrs Gibbons' chief defence lawyer has said he expected her to be pardoned following the peers' visit.
He told the BBC that he had advised his client not to appeal against the verdict or the sentence "for practical and not legal reasons", and she had accepted his advice.
In her first public comment since her arrest, Mrs Gibbons said she had been treated well and made a light-hearted comment that she been given so many apples that she "could set up my own stall".
In a statement made public on Sunday Mrs Gibbons said: "I'm very grateful to all the people working on my behalf. I know so many people out there have done so much.
"I know the Prime Minister has called my son, and I'm really grateful to everyone.
"The guards are constantly asking if I have everything I need. The Sudanese people in general have been pleasant and very generous, and I've had nothing but good experiences during my four months here.
"I'm really sad to leave and if I could go back to work tomorrow then I would."
Mrs Gibbons has not been sent to prison, but instead is being held in a secret location due to fears for her safety.
On Friday crowds of protesters marched in the capital Khartoum demanding a tougher sentence for her alleged crime of blasphemy. Some called for her to be executed by firing squad.