Florence Police Chief Giampaolo Monastra said police received an e-mail on Aug. 20 from the man, Brandon Henry, saying he believed his girlfriend gave birth while visiting Italy and left the newborn in the church.
The baby boy was 2 days old when a nun found him on July 29.
Police in Sugarland, Texas, are investigating on their end, Monastra said, adding that Henry was from the Houston area. Monastra identified the possible mother as Stephany Chavarria, and said in a telephone interview that she had been in Italy with her parents for several weeks.
"We are still investigating, but she could be accused of abandoning a minor," Monastra said, adding authorities have yet to confirm whether Henry or Chavarria is a parent.
"I do think that we will be doing a DNA test to determine the paternity of the child," he said.
Florence police believe the baby was born "either at home or in a hotel," Monastra said, noting that in Italian hospitals all births are registered.
Carmelite nuns at a convent attached to the church have told Italian reporters they noticed a woman with a baby praying shortly before the boy was found. The baby was taken to the hospital for temporary care. Monastra, citing privacy, declined to say where the baby is now.
In cases of abandonment, infants are usually put in foster care until courts determine if they should be put up for adoption.
Monastra said the Texas man told police that when his girlfriend came back from Italy no longer pregnant, she told him that the baby had died.
"We spoke to the purported father by phone and he confirmed everything he had written in the e-mail," Monastra said. He said the woman later told Texas police that she indeed was the mother.