The BBC has said it contacted the family at the centre of the presenter row twice after they made a complaint.
The corporation released a timeline of events, saying a family member of the young person first complained when they attended a BBC building on May 18.
On July 7, The Sun reported allegations made by the family which claimed a BBC presenter paid a teenager for sexually explicit photos.
Two days later the corporation confirmed it had suspended the unnamed presenter.
On May 19, a family member contacted BBC Audience Services and the details of the claims were referred to the BBC’s Corporate Investigations Team, which assessed that the claims did not include an allegation of criminality but nonetheless merited further investigation.
Director-general Tim Davie faced questions about the initial complaint on BBC Radio 4’s World At One programme with broadcaster Sarah Montague on Tuesday.
Mr Davie said: “The facts are there that very simply the Corporate Investigations Team looked at the log – that is the summary of the call – we have clear records of an interaction that lasted 29 minutes.”
The BBC said two subsequent attempts to contact the complainant via phone and email were unsuccessful and while the Corporate Investigations Team was due to return to the matter in the coming weeks, no additional bids to contact the complainant were made after June 6.
The case remained open throughout, the BBC said.
The Sun first contacted the BBC about the allegations it was due to publish on July 6, which was the first time Mr Davie or any executive directors at the BBC were aware of the case.
Mr Davie told the World At One he did not speak to the accused presenter on July 6 and the conversation was conducted by a “senior manager”, which the director-general said was the “right role” for him in being able to oversee the process.
Even in the circumstances where we didn’t have the level of verification we wanted or needed, I do think it is a fair question to review the red flagging process— BBC director-general Tim Davie
The claims made by The Sun last week contained new allegations which were different from the matters being considered by BBC Corporate Investigations, the broadcaster said.
This was the first time the presenter concerned was spoken to about the matter, according to the BBC. The investigations team also contacted the complainant again.
Explaining why no contact was made with the complainant for more than a month, Mr Davie said “thousands” of complaints are made and it is “appropriate” there is a verification process.
He said: “Some verification of that claim is appropriate once the Corporate Investigations team has taken something on. They do some due diligence on what is being alleged.
“Because if we work this through, you’d be in a situation where anyone can ring anything in and you’re taking that straight to presenters or whatever and having that duty of care issue there and a whole load of issues.”
He added: “Even in the circumstances where we didn’t have the level of verification we wanted or needed, I do think it is a fair question to review the red flagging process.”
Mr Davie later added on BBC Radio 4: “I have given a bit of context in terms of the numbers of issues we get coming into our Corporate Investigations unit, over six months that will be about 250, and you take those and they are the serious complaints coming through all different types.”
Asked if the presenter offered to resign, Mr Davie said: “I wouldn’t comment on a private conversation, I think that is in terms of privacy for an individual, I don’t think that’s right.”
Discussing what support the BBC is offering the presenter and if he is concerned about the impact if they are cleared of any wrongdoing, he said: “Duty of care is a very significant factor in this.”
Mr Davie added: “I can’t give you specific details of individuals and duty of care packages. What I can say is the BBC, I think, is excellent at making sure we are offering the right support. We have really good professional teams that do that and it’s one of the highest priorities as we move through this affair.”
The young person told BBC News via a lawyer on Monday nothing inappropriate or unlawful happened with the unnamed presenter and the allegations are “rubbish”.
According to the broadcaster, the legal representative wrote that the young person is estranged from their mother.
The mother and stepfather of the young person stood by their allegation and questioned how their child could afford the lawyer, The Sun reported.
As a result of recent developments, further inquiries are ongoing to establish whether there is evidence of a criminal offence— Police
An unnamed police force has confirmed it was contacted by the parents of the teenager in April, BBC News has reported.
The force said “no criminality was identified” initially, however it has since met with the Metropolitan Police and the BBC, it was alleged.
A statement said: “As a result of recent developments, further inquiries are ongoing to establish whether there is evidence of a criminal offence.”