An Irish online gambling site puts Tettamanzi on top with 5 to 2 odds. But pope predictions are almost always wrong.
His appointment two years ago as archbishop of Milan, Italy's largest diocese, was seen as an endorsement of his candidacy by Pope John Paul II.
In 2001, Tettamanzi defended anti-globalization protesters during a G8 summit and has also been a vocal advocate of the fight against AIDS in Africa.
"A single African child sick with AIDS counts more than the entire universe," he said at the time.
A traditionalist on doctrine, Tettamanzi backed a 1968 encyclical by Pope Paul VI banning artificial birth control.
Despite his conservative views, Tettamanzi is considered a natural mediator with few enemies.
Unusually for a religious leader of his stature, he is not a linguist, and has not travelled outside Italy.