Jenas had his contract terminated for allegedly sending inappropriate messages to a female colleague.
The BBC did not disclose further details about the allegations against him.
The former footballer told The Sun he sent “inappropriate messages” to two colleagues on the One Show, but insisted he “did nothing illegal” and said they were sent to “two consenting adults”.
The presenter added the texts were a “huge error of judgement” for which he was “deeply sorry”, adding that he was “not a sex pest”.
Jenas, who is married with four children, told the paper he was receiving therapy and accepted he “fell below [the] standards” of the BBC.
At the time, talkSport said there were “no plans for Jermaine to broadcast as a presenter on talkSport in the immediate future”.
He said on Friday he was returning to the radio station and would be “doing what I love most, which is talking about football”.
Aherne asked him how he could assure listeners he had changed.
“You need to take responsibility for your actions [and] why you’re in this position,” he said.
“And there’s a reason why this has happened. And once you kind of accept those things, then you can work on yourself and you can work on the other things and you can work on your family and work towards a brighter future.”
When asked about the impact his actions had had on his family, he said he realised “they didn’t deserve to be in that position”.
Jenas added that he intended to “get back on [the] path” of being a role model.
He will return to his job as a football pundit this weekend as co-commentator for Aston Villa vs Tottenham in the FA Cup for talkSport.
Jenas had been hosting talkSport’s drive show when the news of his dismissal from the BBC became public.
