Speaking in Glasgow, the Torchwood actor revealed that he hopes the Twelfth Doctor is female, before name-dropping the comic actress, who played assistant Donna Noble in the sci-fi drama's fourth series.
Barrowman is quoted by PA as saying: "I think that maybe they should go out on a limb next time and try it.
"That always stirs things up a little bit and makes things exciting and it's nice to see different things and challenges happen like that.
"Listen, if Captain Jack can be an omni-sexual time agent and an assistant to The Doctor, why can't we have a female Doctor?"
Meanwhile, Barrowman praised Matt Smith's performance in the current role, but admitted that David Tennant's Tenth Doctor will always be his favourite.
The 44-year-old added: "Matt has put his mark on it and rightfully so and he's a wonderful Doctor, but my Doctor will always be David."
> John Barrowman: 'Torchwood should explore Jack's past'
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Watch Arthur Darvill discuss the end of the current season of Doctor Who with Digital Spy below: