Kamal al-Jazouli, Gibbons' chief defence lawyer, said he believed it was possible she would receive a pardon from Omar Hassan al-Bashir, the Sudanese president.
A source close to the Sudanese government said the two British politicians hoped to meet al-Bashir to discuss the case.
"They have arrived and they have a series of meetings lined up, including with the president," said the official, who gave no further details on the visit with Gibbons.
"An appeal from a fellow Muslim could have an impact." Pardon hopes
Gibbons' lawyers and the British embassy in Sudan have refused to give details of her location after hundreds of Muslims took to the streets of the capital on Friday, many waving swords and green Islamic flags, calling for her death.
Al-Jazouli said she was in a well-guarded location, and away from other prisoners. He was hopeful al-Bashir would pardon her.
|Gibbons was moved away from other inmates|
after protesters called for her death [AFP]
"I have no inside information," he said. "But I think there will be a pardon. The president has the power to change sentences and pardon defendants."
Al-Jazouli said he believed Lord Ahmad, from Britain's ruling Labour party, and Baroness Warsi, an opposition Conservative, have a good chance of success.
"I think the Sudanese government must now be as concerned for her safety as the British government. There are so many factions and sects and the government cannot control them," he said.
"It would be a nightmare for Sudan if anyone harmed her."
Omar Daair, a British embassy spokesman, said Lord Ahmed had flown into Sudan on a personal mission.
"Any efforts in this case are welcome. We have offered to help in any way we can," he said. Animal project
In September, Gibbons allowed her seven-year-old pupils at a Khartoum private school pick their favourite name for a teddy bear as part of a project on animals.
Twenty out of 23 of them chose Mohammad - a popular boy's name in Sudan, as well as the name of Islam's prophet.
Gibbons circulated a letter to parents, telling them that the children would be bringing the teddy bear home at weekends as part of the exercise.
Two months later, a staff member at Unity High School handed the letter to Sudan's ministry of education.
Gibbons was arrested last Sunday and charged on Wednesday with insulting religion, inciting hatred and showing contempt for religious beliefs.
These charges are punishable by up to 40 lashes, a year in prison or a fine. She was convicted of insulting Islam late on Thursday.