But the Council of Islamic Scholars, an influential group in the country, warned the government not to free Gibbons earlier, saying it would "wound the sensibilities of Muslims in Sudan".
Gibbons was sentenced after her class of seven-year-olds named a teddy bear Muhammad, the same name of the prophet of Islam, as part of a school project.
She is due to be deported on December 9 if the British MPs fail to secure a pardon before the sentence deadline.
Ahead of Monday's meeting, Warsi said: "I'm still hopeful ... I understand the cultural and religious sensitivities around Islam but as a British woman I have huge concerns for Gillian.
"This is a huge issue and we must remain optimistic and hopeful that we can resolve it as early as possible."
Britain's ambassador to Sudan, Rosalind Marsden, said the meeting with the president was grounds for optimism.
"We very much hope that following the meeting with the president tomorrow morning the decision will be taken to release Mrs Gibbons as soon as possible," she told reporters.
Mohammed Ibrahim Shoush, a Sudanese political analyst, told Al Jazeera that his country is under great pressure.
He said on the one hand Sudan does not want to appear "weak" and to be bowing to British pressure. But on the other hand, they do not want to sound like "they do not care about religion".
When asked if Gibbons is likely to be released early, Shoush said he thought so.
But Islamic scholars said the government would face problems if it reduced Gibbons' sentence, which they said was too light.
Sheikh Mohammad Abdel Karim, a council spokesman, said: "If the government retracts this judgment ... this would be a very bad precedent and it would have very bad consequences on the reputation of the state ... not only in Sudan but also outside Sudan."
The visit by the Muslim politicians - considered more acceptable negotiating partners for the Khartoum government - came as Gibbons' lawyer said he hoped there would be a presidential pardon.
|Gibbons was moved away from other inmates|
after protesters called for her death [AFP]
"There is a probability she will be released before the end of her sentence," Kamel Jazuli said on Saturday.
"The president has the right to do this for any prisoner and I don't exclude that he will do it."
He added that Gibbons was being held in a clean, well-guarded prison.
The location of the prison, however, remains secret, after t
housands of people demonstrated in Khartoum after Friday prayers against what they view is a lenient sentence, with some calling for her death.
Some protesters brandished ceremonial swords and said she should be put to death.
David Miliband, Britain's foreign secretary, has said the situation was due to an "innocent misunderstanding" and has twice called in Sudan's ambassador to London.