The presenter – who has been on the hit show since 2014 - is well-known for her black bob and thick fringe, a look she has been sporting for years.
But it seems a head honcho thought she needed a bit of a trim when she was being offered her presenting slot on the BBC ballroom show.
According to The Sun, Winkleman told the story at the Edinburgh TV Festival.
The star said that Danny Cohen, who was the controller of BBC One at the time, phoned her up to give her the job – then asked for her hairstylist’s number.
She said that after offering her the job he added: “I’m just going to need a phone number from you.”
“I was like, ‘Oh yeah, OK, which one?’ and he said, ‘Your hairdresser’,” she said.
“I was like, ‘Bit weird, controller of BBC One’.”
Winkleman, 51, said that a couple of days later the person who did her hair told her that “this guy called Danny” had called to complain about the length of her fringe.
She was quoted as saying: “He (Cohen) was like, ‘You can have this job but it’s just annoying, it’s down to your nose. You want to be on telly but you’re invisible’.”
Winkleman joined Strictly for its 12th series.
She and Daly are now preparing for the show's 21st series, which is due to start in September.
Watch: Claudia Winkleman told 'The Traitors' bosses to end the show after the first season