The two countries came to the brink of war earlier this year.
After fighting over oil facilities and disputed land broke out, the United Nations threatened both sides with sanctions if they did not reach a comprehensive agreement.
African Union mediators have yet to confirm that an agreement has been made, but President Omar al-Bashir of Sudan and President Salva Kiir of South Sudan are expected to sign a deal on Thursday.
Many people will be sceptical until they see a deal has actually been signed.
It had been announced that the two presidents would sign a comprehensive agreement on Wednesday morning, but this did not happen.
If this deal is signed, getting the oil flowing again would boost both economies, according to BBC.
Few details have been released, but negotiators for both sides said that a demilitarised border buffer zone between the two countries had been agreed.
They also said that an economic agreement had been reached to allow South Sudan's stalled oil production to be restarted.
But a solution was not found to the disputed flashpoint region of Abyei, or on a series of border zones claimed by both countries.
The prospective deal therefore falls short of the comprehensive agreement called for by the UN.
When South Sudan gained independence in July 2011, it obtained two-thirds of the former country's oil while Sudan retained the processing and export facilities.
No agreement was reached on how much the South should pay Sudan in transit fees.
In January, the South shut down oil production, accusing Sudan of stealing its oil - Sudan said it was owed the money - and the two countries' economies have been seriously damaged as a result.
South Sudan, where people chiefly follow the Christian faith or traditional indigenous religions, fought for decades with mainly Muslim Sudan.