The Sun newspaper had an exclusive interview with the parents
The Press Complaints Commission (PCC) is investigating alleged payments made to the 13-year-old father of a baby girl born last week.
Alfie Patten's girlfriend Chantelle Steadman, 15, gave birth to Maisie last week, and tabloid newspapers have reportedly paid for the couple's story.
The Editor's Code Of Practice says minors cannot be paid for "material involving children's welfare", it said.
The teenage father has said he will support his child and her mother.
The PCC statement said: "Newspapers are allowed to breach this rule if there is a demonstrable public interest.
"The PCC will make a public ruling on the matter when it has completed its investigation. The commission has powers - under which it is conducting this inquiry - to launch investigations of its own volition."
The 13-year-old said on Monday he would be taking a DNA test to prove he is the father of the child after two other teenagers told a Sunday newspaper they had also slept with the baby's mother, who is from Hailsham in East Sussex.
His spokesman Max Clifford said: "They are planning to do a DNA test.
"Alfie believed he was the father but due to reports in the News of the World at the weekend, he wants to make sure by having a DNA test as soon as possible."
East Sussex County Council said the teenage parents had received "a package of support" to help care for Maisie.
"Our primary duty is the protection of children and young people. We do not believe that the interest of the children and young people in this case are being well served by the current media coverage of it.
"We will continue to do our professional job of supporting these children and young people and putting their interests first. And for that reason we will not be commenting on this issue further. We will also being referring the case to the PCC.