Scottish actor Capaldi is appearing in his final series as the Doctor.
He has said whoever replaces him - whether a man or woman - will be "wonderful".
Inverness-born Gillan, who played Amy Pond alongside Matt Smith's Doctor, said she would respect whatever decision was made on the role.
A man has been chosen as Capaldi's successor, according to newspaper reports.
Speaking at the Los Angeles premiere of her latest film, Guardians Of The Galaxy Vol 2, Gillan said: "It's OK, maybe next time.
"I trust the BBC and their choices and they haven't failed us yet with the Doctor.
"But it would be cool to see a woman in the role one day because a woman could absolutely play that role."
The BBC said no casting decisions have been made.
In Guardians of the Galaxy Vol 2, Gillan plays blue-skinned space pirate Nebula.
Former Doctor Who companion Karen Gillan has said an actress succeeding Peter Capaldi in the lead role of the long-running TV series "would be cool".