Now, speaking on BBC Radio show World At One, David has called for bosses to drop Olivia a line, stating: “Olivia would clearly be a magnificent choice. If you have the right people telling the right stories then it’s absolutely a possibility.”
Interestingly, ‘Broadchurch’ writer Chris Chibnall is set to take over from Steven Moffat, and assume the role of ‘Doctor Who’ showrunner for the 2018 series - which means he’ll be leading the search for Peter’s replacement.
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The duo will return for the third and final series of 'Broadchurch' later this month
ITV Pictures
It’s believed that the new Doctor will make their first appearance in this year’s Christmas special, when a regeneration takes place (via Radio Times). Before that, Peter will star in one, final series, which begins airing in April.
And just in case bosses need a few more ideas, we’ve got some of other options they can add to the shortlist…
13 Female Stars Who Could Play The Lead In 'Doctor Who'
Helen Mirren(01 of13)
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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Multi-award winning actress Olivia also made the bookies' shortlist, with odds of 20/1. (credit:Matt Crossick/Matt Crossick)
Hayley Atwell(12 of13)
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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)
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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)