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The 64-year-old cardinal and head of the Vatican's Pontifical Council for Justice and Peace is considered progressive by some supporters, and his mediation during a tight Ghanaian election in 2008 won him high praise.
But his image was marred last year after he showed an alarmist video on Muslim immigration in Europe at a synod. He later apologised.
Turkson is one of two Africans who could replace retiring Pope Benedict XVI, alongside South African Wilfrid Napier. When Benedict announced his resignation, bookmakers gave Turkson good odds at being elected.
Following Benedict's announcement, there have been calls for an African to be elected pope.
Advocates of such a move point out that the Roman Catholic Church has seen rapid growth in Africa -- currently home to some 15 percent of the world's 1.2 billion Catholics -- in contrast to other regions of the world.
Parishioners and clergy remember Turkson as a learned, patient leader for 17 years of Ghana's oldest archdiocese, the archdiocese of Cape Coast.
Supporters shrugged off the video controversy, but were mixed about whether he would be chosen as the first black pope.
"He's a priest for the people. A bishop for the people. A cardinal for the people," said Joseph Ernest Arthur, administrator of St. Frances De Sales Cathedral in Cape Coast.
"And therefore... it is our desire that in the next conclave, he also becomes the pope for the people."
There are about three million Catholics in Ghana, a country of 24 million considered one of the most stable and democratic in West Africa.
Turkson was in charge of the archdiocese of Cape Coast from 1992 to 2009. Those who knew him say they are not surprised that one of their own could be in the running for the top job.
Vicar-general of the archdiocese Isaac Ebo-Blay related the story of Turkson paying a personal late-night visit to a woman who was suffering from breast cancer.
"We went there and his presence touched a woman who was really in pain," Ebo-Blay said. "I was with him that evening and I could see that the visit brought a kind of solace and comfort to the woman."
Arthur meanwhile remembered that Turkson sent a priest to a seminary to study Islam, so the church could better relate to Ghana's 3.8 million Muslims.
During Ghana's 2008 election, when less than one percent of the vote separated two candidates and many feared political violence, Turkson mediated between the two parties, gaining respect for his efforts.
He repeated the peacemaker role in 2011, when Benedict asked him to go to Ivory Coast to mediate between Laurent Gbagbo, who lost a presidential election but refused to concede, and his opponent Alassane Ouattara.
But the violence raging in Ivory Coast that would kill at least 3,000 people meant that Turkson found himself stuck in Ghana, unable to access the neighbouring country's main city Abidjan.
Back in his days in Cape Coast, parishioner Matthew Owusu said you could tell when Turkson, who speaks a number of languages, was holding mass by the occasional Latin word he would throw in.
"He encouraged children and youth to learn Latin," Owusu said. Turkson's personal motto, Owusu said, is "Vivere Christus est," which means "To live is Christ."
But Catholics were divided over whether he will make the cut.
"We all pray so that one day the dream of a black pope becomes real. It is God who ordains," Owusu said. "I think he stands a chance."
Patrick Amedeka, a student at St. Peter's Seminary, where Turkson was once vice-rector, was less hopeful.
"I don't expect that he would be a pope this era," Amedeka said. "I know that the church is a spiritual institution, but it's also a human institution. There are other candidates out there."