Gunmen seized Obodo on Saturday as he arrived in front of a church outside the city of Warri, one of the major cities in Nigeria's Niger Delta, local police spokesman Charles Muka said. The kidnappers made contact with the international football player's family in Warri shortly afterward, making their ransom demand, Muka said.
"We are on the trail of the kidnappers," Muka said Sunday.
Meanwhile, the Nigeria Football Federation issued a statement Sunday calling on kidnappers to release Obodo, who has played for the national team in the past.
"This is a sad thing. Christian Obodo served this country patriotically and without blame when he played for the senior national team, (the) Super Eagles," federation President Aminu Maigari said. "The only thing we can do is to appeal passionately to the kidnappers to let him go. He is a young patriot who should not go through this kind of experience.
Lecce was relegated to a second-tier league this season, while Udinese finished third in Serie A this season.
Kidnappings remain common in the Niger Delta, a region that provides about 2.4 million barrels of oil a day for Nigeria. Gangs and militants once only targeted the foreign oil workers, but in recent years have increasingly gone after middle- and upper-class Nigerians there.
Nigerian football players and their families have been targeted in the past by kidnappers. In August, two Nigerian soldiers and others took part in the kidnapping of Chelsea midfielder John Obi Mikel's father from Jos in central Nigeria, and at one point demanded a $4 billion ransom they considered "chicken change" for the team, officials said. Authorities later traced Mikel's father to the northern city of Kano and freed him.
In 2008, gunmen abducted the younger brother of Everton defender Joseph Yobo as he left a nightclub in Port Harcourt, the delta's largest city. The brother was released unharmed about two weeks later, though it was unclear if a ransom had been paid.