The allegations involve digital communications such as texts, which were raised with the corporation a few weeks ago.
In an interview with talkSport radio, he repeatedly said “I can’t really talk about it” when asked about the claims being made.
“I, as you can probably see, I am not happy about it,” he told the station.
Asked if he was surprised that any complaints had been made against him, Jenas said again: “I can’t really talk right now.”
“I’ve just got to leave this to a team of lawyers at the minute who are, yeah, I suppose just managing the situation,” he said.
“This is… Yeah, it’s tough, you know. But I’ve got to listen to my lawyers.”
A BBC spokesperson said: “We can confirm Jermaine Jenas is no longer part of our presenting line-up.”
He was last on air for the corporation earlier in the summer.
Jenas, who is married and has four children, earned £190,000 – £194,999 at the BBC for his work on the FA Cup, Match of the Day and the World Cup.
His work on The One Show was for BBC Studios, the BBC’s commercial production company, so his salary for that is not in the public domain.
He became a permanent member of the flagship show’s presenting team in 2021, appearing on the sofa beside long-time host Alex Jones.
Jenas also does work for talkSport, and was presenting a show on air when the news broke.
The radio station said it had been made aware of the story as the programme started – but a decision was made “with Jermaine that he should continue to present”.
“Given the array of serious allegations being reported as the story continues to evolve, it’s for Jermaine as a private individual to address them in the way he chooses,” it said.
“There are no plans for Jermaine to broadcast as a presenter on talkSport in the immediate future.”
Jenas is also employed by TNT Sports, a group of paid television sports channels. They told the BBC they were not making any comment.
His profile was removed from his agent’s website on Thursday evening.
Sophie Anderson, a UK-based writer, is your guide to the latest trends, viral sensations, and internet phenomena. With a finger on the pulse of digital culture, she explores what’s trending across social media and pop culture, keeping readers in the know about the latest online sensations.