The BBC insists it has still not chosen a new host for the Radio 2 breakfast show, despite press speculation that Zoe Ball is set to take over the biggest programme in UK radio.

Chris Evans announced this month that he was leaving the programme for Virgin Radio, prompting speculation over who would inherit the slot, which reaches more than 9 million listeners a week.

Ball, a former Radio 1 breakfast show host who presents a weekend show on the station, has been linked to the job. On Monday, the Sun reported that she was in advanced negotiations to take over the programme but no contract had been signed. The newspaper said a key concern was how she would handle her family commitments in Brighton, where she lives and has two children with her former husband Norman Cook.

“We are considering and talking to a number of people,” a BBC spokesperson said. “We haven’t made a decision and we’ll make an announcement when we have.”

Sara Cox, a longtime friend of Ball’s and a former Radio 1 breakfast show host, has also been linked to the job. She presents a late night show on Radio 2.

BBC insiders said the contest remained open and warned against negotiations being carried out through the media.

The station is under pressure to appoint a woman to the job, which has only ever been held by men. It caps a rapid turnover in big BBC breakfast show hosts, with 6 Music recently appointing Lauren Laverne to host the slot and Radio 1 giving the job to Greg James.

Cook was coincidentally being interviewed on Monday morning’s Radio 2 breakfast show by Evans, who said: “I’m going to ask you a question, then you’re going to say: ‘I’m sworn to secrecy’, and then we’re going to move on. So, what do you know of this front-page story in the Sun today about Zoe being offered this show come 2019?”

Cook replied: “I couldn’t possibly comment on that, Christopher.”

• This article was amended on 18 September 2018. An earlier version incorrectly referred to Ball having two sons. This has been changed to “two children”.

