The chairman of the African Union is due to arrive in Kenya as diplomatic moves to try to end the country's political crisis intensify.
Mr Kufuor has experience in Ivory Coast and Liberia
John Kufuor, also Ghana's president, will try to help resolve divisions that erupted after the disputed victory of President Mwai Kibaki in elections.
Opposition head Raila Odinga has said he would only hold direct talks with President Kibaki if Mr Kufuor mediated.
Violent clashes since the 27 December election have left 600 people dead.
The BBC's Will Ross in Ghana's capital, Accra, says that last week Mr Kufuor's proposed visit was blocked so that his arrival on Tuesday is at least a sign that there has been some progress.
Ghana's Minister of Information Oboshie Sai Cofie said Mr Kufuor's role would be more as a facilitator than a mediator - someone to bring the two sides together in a more congenial atmosphere.
Our correspondent says Mr Kufuor is not someone to bash heads together - he is known as the "gentle giant" - and has helped negotiate during the conflicts in Ivory Coast and Liberia.
South African Nobel peace prize laureate, Archbishop Desmond Tutu, and the top US official for Africa, Jendayi Frazer, have also been central to international efforts to find a solution.
But the BBC's Adam Mynott in Nairobi says the positions of Kenya's rivals remain far apart.
Mr Odinga says he was cheated of election victory and has called on Mr Kibaki to stand down.
Mr Kibaki refuses, saying he was rightfully elected.
Our correspondent says Mr Kufuor may be able to reduce tension in Kenya.
After meeting Ms Frazer, Mr Odinga called off planned nationwide rallies, saying he wanted to give international mediation a chance.
Mr Kibaki then invited Mr Odinga to hold their first face-to-face talks since the election on Friday.
But Mr Odinga insists that an international facilitator be present.
Ms Frazer said there may have been vote-rigging by both sides and that ordinary Kenyans had been let down.
"They've been cheated by their political leadership and their institutions," she said.
Some 250,000 people have fled their homes in clashes between rival political supporters, ethnic groups and the police.
Mr Odinga said Kenya was living through the gravest crisis it had faced and condemned the violence that had taken place.
Meanwhile, Mr Kibaki has reconvened parliament for 15 January.
Mr Odinga's Orange Democratic Movement won a majority in parliament but does not have the two-thirds needed for a vote of no-confidence in the president.
Both sides have accused the other of ethnic cleansing during a week of violence after Mr Kibaki was declared the winner.
A government ministry says 486 people have been killed but a senior police officers told the AFP news agency: "We have at least 600 dead... some bodies are still in the bushes where fighting occurred."