The ‘well-known’ star reportedly demanded ‘what have you done?’ in the call, which occurred last week, MailOnline reports.
He also asked his alleged victim to ring their mother to persuade her to ‘stop the investigation’ as he began to panic, according to The Sun.
The BBC confirmed in a public statement this afternoon that it had suspended a male member of staff over the allegations, but has not revealed the identity of the employee.
The family of the teenager, who is now 20, were reportedly upset with the wording of the statement from the broadcaster and claimed they had not been properly contacted.
It comes as the Metropolitan Police confirmed it has spoken to the BBC about the suspended presenter accused of paying a teenager more than £35,000 for sexually explicit images.
Director-general Tim Davie said today that the corporation was investigating ‘swiftly and sensitively’ into the ‘deeply concerning’ claims following urgent talks with the government.
It came just hours after Culture Secretary Lucy Frazer held urgent talks with BBC director-general Tim Davie about the scandal, which was first reported to the broadcaster seven weeks ago.
The Daily Mail has been told Mr Davie was not made aware of the allegations until last Thursday, despite claims the teenager’s mother initially contacted the BBC on May 19.
Senior sources said bosses did not at first ‘register the seriousness of it’.
A separate BBC source said: ‘There are layers to what the police want and need to take it further – we may get to that stage, we may not.’
The under-fire presenter’s colleagues are said to be appalled by the situation, while growing increasingly dismayed at how the BBC has handled the crisis.
One said last night: ‘We are all aghast. And at the moment it’s like the plane is on fire but the cockpit door is locked. We just have to hope the pilot is doing something.’
However the Met said the broadcaster has not yet made a ‘formal referral or allegation’.
In a statement a spokesperson for the force said: ‘The Met has received initial contact from the BBC in relation to this matter but no formal referral or allegation has been made.
‘We will require additional information before determining what further action should follow.’
In a follow-up email sent to staff, Mr Davie reiterated that the BBC is taking the allegations ‘incredibly seriously’.
Later in the internal email, he adds: ‘By law, individuals are entitled to a reasonable expectation of privacy, which is making this situation more complex. I also want to be very clear that I am wholly condemning the unsubstantiated rumours being made on the internet about some of our presenting talent.
We are in contact with the family referenced in the media reports. I want to assure you that we are working rapidly to establish the facts and to ensure that these matters are handled fairly and with care, including by external authorities where appropriate.’