Speaking with Graham Norton for Virgin Radio about her new film Till, Goldberg admitted that while she is busy, "if a random Doctor Who came along, I could do it".
Goldberg then said she understood she was "not going to be the new black Doctor Who", and when Norton suggested she could play a character related to the Doctor, Goldberg said: "I think I could be Who's cousin!"
You can watch the full clip here. Goldberg and Norton speak about Doctor Who from 8:35.
Doctor Who has seen numerous big casting reveals of late, as filming is currently underway on the show's upcoming 14th season, starring Ncuti Gatwa as the Fifteenth Doctor.
Not only was Millie Gibson unveiled late last year as new companion Ruby Sunday, but Aneurin Barnard was recently announced as new character Roger ap Gwilliam (who appears to be a politician).
Meanwhile Jemma Redgrave is also set to return as Kate Lethbridge-Stewart, meaning her character will have appeared alongside four separate Doctors - Matt Smith's Eleventh Doctor, Peter Capaldi's Twelfth, Jodie Whittaker's Thirteenth and Gatwa's Fifteenth.
She is not currently expected to appear in this year's 60th anniversary specials, which will feature David Tennant back in the title role as the new Fourteenth Doctor, following his return last year at the end of The Power of the Doctor.
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Doctor Who is available to stream on BBC iPlayer with episodes of the classic series also available on BritBox – you can sign up for a 7-day free trial here.
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