Billie, who played the Doctor’s companion Rose Tyler between 2005 and 2008, says it would “feel like a snub” if a woman wasn’t cast in the role.
She told the BBC: “I’ve always supported the original format but I don’t know where they can go from here.
“I think it would be great [to have a female Doctor] given the spirit of the world at the moment. I think it would be timely”.
But despite her comments, it doesn’t sound like Billie will be throwing her hat into the ring.
“I don’t know,” she said. “It’s a lot of work. It would be a lot of time in Cardiff.”
Open Image Modal
Billie as Rose, with former Doctor, Christopher Eccleston
BBC
Billie’s views are supported by Labour’s former Deputy Leader, Harriet Harman, who said she also believed the next Doctor should be a woman.
Speaking at a Press Gallery lunch in the Commons on Tuesday, she said: “He was excellent, Peter Capaldi. Of course there should be a female Doctor Who but what we need is a man as her assistant. She’s got to tell him what to do.”
“I feel sad, I love Doctor Who, it is a fantastic programme to work on.
“I can’t praise the people I work with more highly, but I have always been someone that did a lot of different things.”
Open Image Modal
Off to pastures new: Peter Capaldi
Stuart C. Wilson via Getty Images
The Glasgow-born star, who is the 12th actor to play the Doctor, said his final ever scenes will air at Christmas, but reassured fans that he was still Doctor Who at the moment, as filming was still underway.
The new series is set to return to BBC One in April.
See our pick of the female stars who we think would make great Doctors, in our gallery below...
13 Female Stars Who Could Play The Lead In 'Doctor Who'
Helen Mirren(01 of13)
Open Image Modal
Peter Capaldi is proof that an older star can be perfect in the show's lead role, and anything that means we get more Helen in our lives can only be a good thing. (credit:Ian West/PA Wire)
Janelle Monae(02 of13)
Open Image Modal
Janelle has only just turned her hand to acting, but as anyone who has seen 'Hidden Figures' can confirm, she's certainly something special.
Might the BBC be aiming a little high if they tried to sign up the Screen Actors' Guild award winner? Yes. Does that mean they shouldn't try? Absolutely not. (credit:Matt Sayles/AP)
Rebecca Root(03 of13)
Open Image Modal
We're still disappointed that Rebecca's show 'Boy Meets Girl' won't be returning, but landing this role would make up for it. (credit:Karwai Tang via Getty Images)
Vicky McClure(04 of13)
Open Image Modal
Vicky has proved she's got what it takes to tackle huge roles, thanks to her parts in 'This Is England' and 'Line Of Duty', but we'd love to see her take on something with a fun side. (credit:Anthony Harvey via Getty Images)
Jenna Coleman(05 of13)
Open Image Modal
Jenna served as the Doctor's loyal assistant for three years, but in the world of science fiction, anything is possible and we're sure the writing team could cleverly come up with a way to put her front and centre. (credit:Matt Crossick/PA Wire)
Samira Wiley(06 of13)
Open Image Modal
Samira is no stranger to television, having starred as Poussey Washington in four seasons of 'Orange Is The New Black'. (credit:Dan MacMedan via Getty Images)
Joanne Froggatt(07 of13)
Open Image Modal
We haven't seen enough of Joanne since 'Downton Abbey' came to an end, and the Tardis would certainly be a departure from the drab and dingy servant's quarters her character Anna was used to. (credit:David Livingston via Getty Images)
Susan Wokoma(08 of13)
Open Image Modal
2017 is being billed as Susan's breakthrough year, but her CV is already more-than-impressive, thanks to roles in shows such as 'Misfits', and films 'Burn, Burn, Burn' and 'The Inbetweeners 2'. (credit:Eamonn M. McCormack via Getty Images)
Sian Brooke(09 of13)
Open Image Modal
Sian made her mark on 2017's 'Sherlock', playing a master of disguise. Quite frankly, if she can morph into four different personas with such ease, the role of the Time Lord would be a walk in the park. (credit:Eamonn M. McCormack via Getty Images)
Antonia Thomas(10 of13)
Open Image Modal
Antonia is another star who found fame on E4, playing the feisty Alisha in 'Misfits' - which also gave her a taste for the perils of time travel. (credit:Doug Peters/Doug Peters)
Olivia Colman(11 of13)
Open Image Modal
Multi-award winning actress Olivia also made the bookies' shortlist, with odds of 20/1. (credit:Matt Crossick/Matt Crossick)
Hayley Atwell(12 of13)
Open Image Modal
Hayley was vocal about the fact she wanted the role back in August 2015. Her comments came at an interesting time, as 'Doctor Who' writer AL Kennedy had just claimed that the Doctor should never be a woman. (credit:Eric Catarina via Getty Images)
Lara Pulver(13 of13)
Open Image Modal
When Capaldi announced his decision to step down from the role, bookies soon named Lara the female favourite for the role, offering odds of 10/1. (credit:Dominic Lipinski/PA Archive)