A number of claims were made about Nolan in The Irish News on Tuesday, including that he had sent the image of reality TV star Stephen Bear in 2016.
It was reported that Nolan shared the image when he had wanted to book Bear as a guest on his TV show.
Bear, a former Celebrity Big Brother winner, was jailed for 21 months earlier this year after being convicted of revenge porn and voyeurism.
Addressing the allegations on his morning radio show on Radio Ulster on Friday, Nolan said: “We have had days, as you probably know, of headlines about me and the Nolan team in the papers this week.
“I am not ignoring the story. It is just that the BBC has processes in place to deal with staff complaints and I do need to totally respect those processes.
“They have got to be confidential for them to work.
“I can say one thing though and it is that I am sorry.
“There was a photograph, it was widely available on the internet and I was talking to a long-term friend and peer outside of work.
“I am deeply sorry.”
Nolan rejected an allegation that he or his team manipulate programmes by planting producers in the studio audience.
He said: “I am telling you now, and I can say this on the record, that is completely, categorically false. We do not do that in the Nolan team.
“We value our relationship with you far too much to compromise it.”
Nolan is the fifth-highest paid talent with the BBC, earning between £400,000–£404,999.
The Irish News also said that a former member of staff had made a claim of bullying and harassment against Nolan which was not upheld, and that messages between team members on programmes associated with the star presenter included abusive remarks about politicians.
In a statement earlier this week, BBC Northern Ireland’s director Adam Smyth said: “There are important considerations of fairness and confidentiality involved in the handling of any workplace-related complaint.
“We take these obligations seriously – and in the interests of everyone involved.
“It is for these reasons that we cannot comment on the specifics of any individual case, who/what it may have involved or its outcome.”