The clip contains dialogue from Tom Baker's time as the Doctor, ending with the line: "Don't you forget me."
Doctor Who returns to BBC One and BBC America on Saturday, November 23 for its 50th anniversary special.
Since Matt Smith announced that he would be leaving the show after this year's Christmas special, stars linked to the lead role have included Homeland's David Harewood, The Hour's Julian Rhind-Tutt, The White Queen's Aneurin Barnard and Skyfall's Ben Whishaw.
Dame Helen Mirren recently ruled herself out for the part, and said that she would like to see a gay, black, female Doctor next.
A reconstruction of the First Doctor's TARDIS from Doctor Who went on display at Comic Con in Paris this week.
Watch Digital Spy's Doctor Who Geek TV special on the departure of Matt Smith below: