As the subject of the long-running sci-fi show came up, Miller revealed: "I'd have loved to have been Doctor Who.
"I was once approached and asked if I would be interested in being Doctor Who – this is going back a few years – and I said yes, I would be interested.
"At which point I never heard anything else ever again, and Doctor Who became more and more successful without me."
Miller did later go on to appear on the show with Coleman where he played the Sherrif of Nottingham when Peter Capaldi was the Doctor.
The comedian did go on to note that there is 'still time' for him to be cast as the Doctor, a role currently played by David Tennant after he returned to the series for its 60th anniversary to portray the 14th Doctor.
When Tennant eventually regenerates after the three 60th anniversary specials, he will be replaced by Sex Education star Nguti Gatwa.
Though Jodie Whittaker's last episode saw an array of past Doctor Who actors including Paul McGann and Colin Baker make guest appearances, one past Doctor is not in a hurry to return to the role.
Peter Capaldi, who played the 12th Doctor, recently said he felt he had "sort of done my time on it" and was in favour of "the idea that you leave that as it is, instead of constantly digging up more of it".
Doctor Who is currently available to stream on BBC iPlayer while classic episodes are available on BritBox.
Watch below: Jodie Whittaker regenerates back into David Tennant on Doctor Who