The 27-year-old actor, who plays the 11th incarnation of The Doctor, has already suggested the idea to head writer Steven Moffat.
He told TV Times: "I'd like Eric to do one and I've mentioned it to Steven Moffat. Eric's got to be bad!"
Doctor Who concludes with 'The Big Bang' this Saturday from 6.05pm on BBC One.
> Matt Smith reveals Moffat's 'Who' vision