However, Downing Street refused to confirm if the conversation took place when contacted by MailOnline today or, if it did, what was said.
She added that the relaxed picture was in-keeping with the spirit of the event.
The Dane, who is married to former Labour Party leader Neil Kinnock's son Stephen, 42, has enjoyed a glamorous reputation in her native country since becoming prime minister in 2011.
She said: 'There were lots of pictures taken that day, and I just thought it was a bit of fun.
'Maybe it also shows that when we meet heads of state and government, we too are just people who have fun.'
In an interview with Danish Daily Berlinske, she added: 'There was a sadness, but it was basically a festive event that also celebrated a man who has lived for 95 years and achieved so much in his life.
'There was dancing on the stands. And then we took a really fun selfie.'
Obama, Cameron and Thorning-Schmidt were captured taking the picture at the FNB Stadium near Johannesburg on Tuesday, as thousands of mourners gathered to pay tribute to Nelson Mandela.
The photograph was taken shortly after President Obama gave a rousing speech about the former South African President and civil rights campaigner who died aged 95.
The White House has not commented on the photograph, but David Cameron this week brushed off the incident.
During Prime Minister's Questions in the House of Commons he said: 'In my defense, I would say that Nelson Mandela played an extraordinary role in his life and in his death in bringing people together.
So of course when a member of the Kinnock family asked me for a photograph, I thought it was only polite to say yes.'
But the controversy is not going away as quickly as the world leaders would like.
It led to a backlash from Twitter users who said it was inappropriate behaviour at an event to remember the life of the anti-apartheid hero.
Twitter user James Armitage wrote: 'What selfish morons take a "selfie" at a memorial service? Oh yeah that's right, Barack Obama and David Cameron.'
In a message directed at Mr Cameron, Sarah McDermott said: 'You have precisely zero class or decorum.'
- Independent UK